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| amir dembo probability theory: Probability Theory: STAT310/MATH230 Amir Dembo, 2014-10-24 Probability Theory: STAT310/MATH230By Amir Dembo |
| amir dembo probability theory: Large Deviations Techniques and Applications Amir Dembo, Ofer Zeitouni, 2009-11-03 Large deviation estimates have proved to be the crucial tool required to handle many questions in statistics, engineering, statistial mechanics, and applied probability. Amir Dembo and Ofer Zeitouni, two of the leading researchers in the field, provide an introduction to the theory of large deviations and applications at a level suitable for graduate students. The mathematics is rigorous and the applications come from a wide range of areas, including electrical engineering and DNA sequences. The second edition, printed in 1998, included new material on concentration inequalities and the metric and weak convergence approaches to large deviations. General statements and applications were sharpened, new exercises added, and the bibliography updated. The present soft cover edition is a corrected printing of the 1998 edition. |
| amir dembo probability theory: Lectures on Probability Theory and Statistics Amir Dembo, Tadahisa Funaki, 2005-11-03 This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo’s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup random fractals, the multi-scale truncated second moment and the Ciesielski-Taylor identities are explored. Tadahisa Funaki’s course reviews recent developments of the mathematical theory on stochastic interface models, mostly on the so-called \nabla \varphi interface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques. |
| amir dembo probability theory: In and Out of Equilibrium 2 Vladas Sidoravicius, Maria Eulália Vares, 2008-11-26 This volume consists of a collection of invited articles, written by some of the most distinguished probabilists, most of whom have been personally responsible for advances in the various subfields of probability. |
| amir dembo probability theory: An Invitation to Modern Number Theory Steven J. Miller, Ramin Takloo-Bighash, 2020-07-21 In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class. |
| amir dembo probability theory: Random Polynomials A. T. Bharucha-Reid, M. Sambandham, 2014-05-10 Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Random Polynomials focuses on a comprehensive treatment of random algebraic, orthogonal, and trigonometric polynomials. The publication first offers information on the basic definitions and properties of random algebraic polynomials and random matrices. Discussions focus on Newton's formula for random algebraic polynomials, random characteristic polynomials, measurability of the zeros of a random algebraic polynomial, and random power series and random algebraic polynomials. The text then elaborates on the number and expected number of real zeros of random algebraic polynomials; number and expected number of real zeros of other random polynomials; and variance of the number of real zeros of random algebraic polynomials. Topics include the expected number of real zeros of random orthogonal polynomials and the number and expected number of real zeros of trigonometric polynomials. The book takes a look at convergence and limit theorems for random polynomials and distribution of the zeros of random algebraic polynomials, including limit theorems for random algebraic polynomials and random companion matrices and distribution of the zeros of random algebraic polynomials. The publication is a dependable reference for probabilists, statisticians, physicists, engineers, and economists. |
| amir dembo probability theory: Probability Theory Achim Klenke, 2007-12-31 Aimed primarily at graduate students and researchers, this text is a comprehensive course in modern probability theory and its measure-theoretical foundations. It covers a wide variety of topics, many of which are not usually found in introductory textbooks. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation. |
| amir dembo probability theory: Elements of Information Theory Thomas M. Cover, Joy A. Thomas, 2012-11-28 The latest edition of this classic is updated with new problem sets and material The Second Edition of this fundamental textbook maintains the book's tradition of clear, thought-provoking instruction. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory. All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points. The Second Edition features: * Chapters reorganized to improve teaching * 200 new problems * New material on source coding, portfolio theory, and feedback capacity * Updated references Now current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications. |
| amir dembo probability theory: Superconcentration and Related Topics Sourav Chatterjee, 2014-01-09 A certain curious feature of random objects, introduced by the author as “super concentration,” and two related topics, “chaos” and “multiple valleys,” are highlighted in this book. Although super concentration has established itself as a recognized feature in a number of areas of probability theory in the last twenty years (under a variety of names), the author was the first to discover and explore its connections with chaos and multiple valleys. He achieves a substantial degree of simplification and clarity in the presentation of these findings by using the spectral approach. Understanding the fluctuations of random objects is one of the major goals of probability theory and a whole subfield of probability and analysis, called concentration of measure, is devoted to understanding these fluctuations. This subfield offers a range of tools for computing upper bounds on the orders of fluctuations of very complicated random variables. Usually, concentration of measure is useful when more direct problem-specific approaches fail; as a result, it has massively gained acceptance over the last forty years. And yet, there is a large class of problems in which classical concentration of measure produces suboptimal bounds on the order of fluctuations. Here lies the substantial contribution of this book, which developed from a set of six lectures the author first held at the Cornell Probability Summer School in July 2012. The book is interspersed with a sizable number of open problems for professional mathematicians as well as exercises for graduate students working in the fields of probability theory and mathematical physics. The material is accessible to anyone who has attended a graduate course in probability. |
| amir dembo probability theory: Large Deviations Frank Hollander, 2000 Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems. |
| amir dembo probability theory: The Probabilistic Method Noga Alon, Joel H. Spencer, 2015-11-02 Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley. |
| amir dembo probability theory: In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius Maria Eulália Vares, Roberto Fernández, Luiz Renato Fontes, Charles M. Newman, 2021-03-25 This is a volume in memory of Vladas Sidoravicius who passed away in 2019. Vladas has edited two volumes appeared in this series (In and Out of Equilibrium) and is now honored by friends and colleagues with research papers reflecting Vladas' interests and contributions to probability theory. |
| amir dembo probability theory: Lectures on Probability Theory and Statistics Amir Dembo, Tadahisa Funaki, 2005-11-03 This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo’s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup random fractals, the multi-scale truncated second moment and the Ciesielski-Taylor identities are explored. Tadahisa Funaki’s course reviews recent developments of the mathematical theory on stochastic interface models, mostly on the so-called \nabla \varphi interface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques. |
| amir dembo probability theory: Applied Analysis John K. Hunter, Bruno Nachtergaele, 2001 This book provides an introduction to those parts of analysis that are most useful in applications for graduate students. The material is selected for use in applied problems, and is presented clearly and simply but without sacrificing mathematical rigor. The text is accessible to students from a wide variety of backgrounds, including undergraduate students entering applied mathematics from non-mathematical fields and graduate students in the sciences and engineering who want to learn analysis. A basic background in calculus, linear algebra and ordinary differential equations, as well as some familiarity with functions and sets, should be sufficient.-- |
| amir dembo probability theory: Advanced Classical and Quantum Probability Theory with Quantum Field Theory Applications Harish Parthasarathy, 2022-12-23 This book is based on three undergraduate and postgraduate courses taught by the author on Matrix theory, Probability theory and Antenna theory over the past several years. It discusses Matrix theory, Probability theory and Antenna theory with solved problems. It will be useful to undergraduate and postgraduate students of Electronics and Communications Engineering. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan). |
| amir dembo probability theory: Probability Theory of Classical Euclidean Optimization Problems Joseph E. Yukich, 2006-11-14 This monograph describes the stochastic behavior of the solutions to the classic problems of Euclidean combinatorial optimization, computational geometry, and operations research. Using two-sided additivity and isoperimetry, it formulates general methods describing the total edge length of random graphs in Euclidean space. The approach furnishes strong laws of large numbers, large deviations, and rates of convergence for solutions to the random versions of various classic optimization problems, including the traveling salesman, minimal spanning tree, minimal matching, minimal triangulation, two-factor, and k-median problems. Essentially self-contained, this monograph may be read by probabilists, combinatorialists, graph theorists, and theoretical computer scientists. |
| amir dembo probability theory: Concentration of Measure for the Analysis of Randomized Algorithms Devdatt P. Dubhashi, Alessandro Panconesi, 2009-06-15 This book presents a coherent and unified account of classical and more advanced techniques for analyzing the performance of randomized algorithms. |
| amir dembo probability theory: Lectures on Probability Theory and Statistics Simon Tavaré, Ofer Zeitouni, 2004-01-30 This volume contains lectures given at the 31st Probability Summer School in Saint-Flour (July 8-25, 2001). Simon Tavaré’s lectures serve as an introduction to the coalescent, and to inference for ancestral processes in population genetics. The stochastic computation methods described include rejection methods, importance sampling, Markov chain Monte Carlo, and approximate Bayesian methods. Ofer Zeitouni’s course on Random Walks in Random Environment presents systematically the tools that have been introduced to study the model. A fairly complete description of available results in dimension 1 is given. For higher dimension, the basic techniques and a discussion of some of the available results are provided. The contribution also includes an updated annotated bibliography and suggestions for further reading. Olivier Catoni's course appears separately. |
| amir dembo probability theory: The Random Matrix Theory of the Classical Compact Groups Elizabeth S. Meckes, 2019-08 Provides a comprehensive introduction to the theory of random orthogonal, unitary, and symplectic matrices. |
| amir dembo probability theory: Large Deviations For Performance Analysis Adam Shwartz, Alan Weiss, 1995-09-01 This book consists of two synergistic parts. The first half develops the theory of large deviations from the beginning (iid random variables) through recent results on the theory for processes with boundaries, keeping to a very narrow path: continuous-time, discrete-state processes. By developing only what is needed for the applications, the theory is kept to a manageable level, both in terms of length and in terms of difficulty. Within its scope, the treatment is detailed, comprehensive and self-contained. As the book shows, there are sufficiently many interesting applications of jump Markov processes to warrant a special treatment. The second half is a collection of applications developed at Bell Laboratories. The applications cover large areas of the theory of communication networks: circuit-switched transmission, packet transmission, multiple access channels, and the M/M/1 queue. Aspects of parallel computation are covered as well: basics of job allocation, rollback-based parallel simulation, assorted priority queueing models that might be used in performance models of various computer architectures, and asymptotic coupling of processors. These applications are thoroughly analyzed using the tools developed in the first half of the book. Features: A transient analysis of the M/M/1 queue; a new analysis of an Aloha model using Markov modulated theory; new results for Erlang's model; new results for the AMS model; analysis of serve the longer queue, join the shorter queue and other simple priority queues; and a simple analysis of the Flatto-Hahn-Wright model of processor-sharing. |
| amir dembo probability theory: Analysis II Terence Tao, 2016-09-26 This is part two of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory. |
| amir dembo probability theory: Random Surfaces Scott Sheffield, 2005 The author develops a general theory of discrete and continuous height models governed by Gibbs potentials that depend only on height differences. He characterizes the gradient phases of a given slope as minimizers of specific free energy and gives large deviation principles for surface shapes and empirical measures. For convex, nearest neighbor Gibbs potentials, he shows that gradient phases are characterized by their slopes and, in higher dimensional discrete settings, by one additional parameter. For standard $2+1$ dimensional crystal surface models, he shows that all smooth phases (crystal facets) lie in the dual of the lattice of translation invariance. |
| amir dembo probability theory: The Normal Distribution Wlodzimierz Bryc, 2012-12-06 This book is a concise presentation of the normal distribution on the real line and its counterparts on more abstract spaces, which we shall call the Gaussian distributions. The material is selected towards presenting characteristic properties, or characterizations, of the normal distribution. There are many such properties and there are numerous rel evant works in the literature. In this book special attention is given to characterizations generated by the so called Maxwell's Theorem of statistical mechanics, which is stated in the introduction as Theorem 0.0.1. These characterizations are of interest both intrin sically, and as techniques that are worth being aware of. The book may also serve as a good introduction to diverse analytic methods of probability theory. We use characteristic functions, tail estimates, and occasionally dive into complex analysis. In the book we also show how the characteristic properties can be used to prove important results about the Gaussian processes and the abstract Gaussian vectors. For instance, in Section 5.4 we present Fernique's beautiful proofs of the zero-one law and of the integrability of abstract Gaussian vectors. The central limit theorem is obtained via characterizations in Section 7.3. |
| amir dembo probability theory: Contracting Over Actions Alexander Philip Frankel, 2011 I consider models in which contracts are written over the verifiable actions taken by an agent in multiple decisions. The principal's preferences over actions depend on underlying states of the world, but only the agent observes the states. The principal cannot audit the agent's information or punish her ex post for having taken inappropriate actions. Moreover, the principal is uncertain about the agent's preferences conditional on the states. Chapter 2 extends the concept of a quota contract to account for discounting and for the possibility of infinitely many periods: a discounted quota fixes the number of expected discounted plays on each action. Discounted quotas are optimal contract forms, even if arbitrary dynamic transfer payments are available, if the agent is assumed to have state-independent preferences. I recursively characterize the optimal discounted quotas for an infinitely repeated problem with independent and identically distributed states. Then I give a more explicit description of these contracts in the limit as interactions become frequent, and when only two actions are available. In Chapter 3 I allow the agent's preferences to depend on the states of the world. Under a variety of assumptions on the timing of the game and on the set of possible agent utility functions, I solve for the max-min optimal mechanisms -- those which maximize the principal's payoff against the worst possible agent preference type. These mechanisms are characterized by a property which I call aligned delegation. Max-min optimal mechanisms may take the simple forms of simultaneous ranking mechanisms, sequential quotas, or budgets. |
| amir dembo probability theory: Two-Dimensional Random Walk Serguei Popov, 2021-03-18 The main subject of this introductory book is simple random walk on the integer lattice, with special attention to the two-dimensional case. This fascinating mathematical object is the point of departure for an intuitive and richly illustrated tour of related topics at the active edge of research. It starts with three different proofs of the recurrence of the two-dimensional walk, via direct combinatorial arguments, electrical networks, and Lyapunov functions. After reviewing some relevant potential-theoretic tools, the reader is guided toward the relatively new topic of random interlacements - which can be viewed as a 'canonical soup' of nearest-neighbour loops through infinity - again with emphasis on two dimensions. On the way, readers will visit conditioned simple random walks - which are the 'noodles' in the soup - and also discover how Poisson processes of infinite objects are constructed and review the recently introduced method of soft local times. Each chapter ends with many exercises, making it suitable for courses and independent study. |
| amir dembo probability theory: Probability Rick Durrett, 2010-08-30 This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject. |
| amir dembo probability theory: The Geometry of Random Fields Robert J. Adler, 1981-01-01 Originally published in 1981, The Geometry of Random Fields remains an important text for its coverage and exposition of the theory of both smooth and nonsmooth random fields; closed form expressions for the various geometric characteristics of the excursion sets of smooth, stationary, Gaussian random fields over N-dimensional rectangles; descriptions of the local behavior of random fields in the neighborhoods of high maxima; and a treatment of the Markov property for Gaussian fields. Audience: researchers in probability and statistics, with no prior knowledge of geometry required. Since the book was originally published it has become a standard reference in areas of physical oceanography, cosmology, and neuroimaging. It is written at a level accessible to nonspecialists, including advanced undergraduates and early graduate students. |
| amir dembo probability theory: Gibbs Measures and Phase Transitions Hans-Otto Georgii, 2011 From a review of the first edition: This book [...] covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics. [...] It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. (F. Papangelou |
| amir dembo probability theory: An Introduction to Measure Theory Terence Tao, 2021-09-03 This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book. |
| amir dembo probability theory: The Theory of Matrices Peter Lancaster, Miron Tismenetsky, 1985-05-28 Matrix algebra; Determinants, inverse matrices, and rank; Linear, euclidean, and unitary spaces; Linear transformations and matrices; Linear transformations in unitary spaces and simple matrices; The jordan canonical form: a geometric approach; Matrix polynomials and normal forms; The variational method; Functions of matrices; Norms and bounds for eigenvalues; Perturbation theory; Linear matrices equations and generalized inverses; Stability problems; Matrix polynomials; Nonnegative matrices. |
| amir dembo probability theory: Waves and Optics Harish Parthasarathy, 2021-02-07 This book covers all aspects of waves and optics ranging from one dimensional waves in a vibrating string, two dimensional waves in a vibrating membrane, both of which are transverse, three dimensional electromagnetic waves generated by radiating antennas and longitudinal sound/pressure waves in an air column. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka. |
| amir dembo probability theory: Probability Geoffrey Grimmett, Dominic Welsh, 2014-08-21 Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem. There is an account of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process. The final chapter is a fairly extensive account of Markov chains in discrete time. This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities. |
| amir dembo probability theory: Random Walks and Heat Kernels on Graphs M. T. Barlow, 2017-02-23 Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs. |
| amir dembo probability theory: Random Graphs and Complex Networks Remco van der Hofstad, 2017 This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises. |
| amir dembo probability theory: Two Models of Probability Theory Alan Michael Hammond, 2005 |
| amir dembo probability theory: Mathematical Foundations of Infinite-Dimensional Statistical Models Evarist Giné, Richard Nickl, 2016 This book develops the theory of statistical inference in statistical models with an infinite-dimensional parameter space, including mathematical foundations and key decision-theoretic principles. |
| amir dembo probability theory: Real Analysis Elias M. Stein, Rami Shakarchi, 2005-04-03 Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels. Also available, the first two volumes in the Princeton Lectures in Analysis: |
| amir dembo probability theory: Interacting Particle Systems Thomas M. Liggett, 2006-01-09 From the reviews [...] This book presents a complete treatment of a new class of random processes, which have been studied intensively during the last fifteen years. None of this material has ever appeared in book form before. ...The high quality of this work, [...] , makes a fascinating subject and its open problem as accessible as possible. [...] F.L. Spitzer in Mathematical Reviews, 1986 [...] However, it can be said that the author has succeeded in what even experts are seldom able to achieve: To write a clearcut and inspiring book on his favorite subject which meets most, if not all requirements which can be imposed on a comprehensive text on an important new field. The author can be congratulated on his excellent presentation of the theory of interacting particle systems. The book is highly recommended to everyone who works on or is interested in this subject: to probabilists, physicists and theoretical biologists. [...] G. Rosenkranz in Methods of Information in Medicine, 1986 |
| amir dembo probability theory: Large Deviations and Applications S. R. S. Varadhan, 1984-01-01 Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small. |
Probability Theory: STAT310/MATH230 March 15, 2023
This chapter is devoted to the mathematical foundations of probability theory. Section 1.1 introduces the basic measure theory framework, namely, the probability space and the ˙ …
Stats 310A Session Notes - Yu Bai
This note contains Section materials for Stats 310A (Probability Theory I), Fall 2017 at Stanford University. Most of the materials follow the development of Dembo [2] and Billingsley [1].
Amir Dembo - Stanford University
ANNALS OF PROBABILITY Dembo, A., Peres, Y., Rosen, J. Model-free distributed learning. IEEE transactions on neural networks.
Title: Persistence Probabilities Amir Dembo, Stanford …
Amir Dembo, Stanford University . Persistence probabilities concern how likely it is that a stochastic . process has a long excursion above fixed level and of what are the . relevant...
Probability Theory: STAT310/MATH230 April15,2021
This chapter is devoted to the mathematical foundations of probability theory. Section 1.1 introduces the basic measure theory framework, namely, the probability space and the σ …
Gibbs Measures and Phase Transitions on Sparse Random …
Amir Dembo ∗, Andrea Montanari ∗ Stanford University. e-mail: amir@math.stanford.edu; montanari@stanford.edu Abstract: Many problems of interest in computer science and informa …
Homework 8 - Stanford University
Solve Exercises [3.3.10], [3.3.21], [3.3.23], in Amir Dembo’s lecture notes. An exercise on weak convergence of measures Let = f0;1gN be the set of (in nite) binary sequences != (! 1;! 2;! …
Large Deviations Techniques And Applications Amir Dembo …
probability Amir Dembo and Ofer Zeitouni two of the leading researchers in the field provide an introduction to the theory of large deviations and applications at a level suitable for graduate …
SPECTRAL MEASURE OF LARGE RANDOM HANKEL, MARKOV …
WLODZIMIERZˆ BRYC, AMIR DEMBO, AND TIEFENG JIANG Abstract. We study the limiting spectral measure of large symmetric random matrices of linear algebraic structure. For Hankel …
Midterm - web.stanford.edu
Let (Ω, F, P) be a probability space, denote by L2(Ω, F, P) the vector space of square integrable random variables. Given X1, . . . , Xn ∈ L2(Ω, F, P), let W({Xi}i∈[n]) be the vector space of …
MATH-60051 and MATH-70051 Probability Theory I Fall 2006.
• Amir Dembo, Probability Theory • Varadhan, Probability Theory, (Ch. 1 – 3.6). Other books: • R.M. Dudley Real Analysis and Probability. Best account of the func-tional analysis and metric …
Probability Theory: STAT310/MATH230; September 12, 2010
This chapter is devoted to the mathematical foundations of probability theory. Section 1.1 introduces the basic measure theory framework, namely, the probability space and the ˙ …
Homework 7 - Stanford University
Solve Exercises [3.2.8], [3.2.9], [3.2.13], [3.2.26], [3.2.14] in Amir Dembo's lecture notes.
Practice Final - Stanford University
You can cite theorems (propositions, corollaries, lemmas, etc.) from Amir Dembo’s lecture notes by number, and exercises you have done as homework by number as well. Any other non …
Large Deviations Techniques And Applications Amir Dembo …
probability Amir Dembo and Ofer Zeitouni two of the leading researchers in the field provide an introduction to the theory of large deviations and applications at a level suitable for graduate …
Large Deviations Techniques And Applications Stochastic …
probability. Amir Dembo and Ofer Zeitouni, two of the leading researchers in the field, provide an introduction to the theory of large deviations and applications at a level suitable for graduate …
CURRICULUM VITAE - adembo.su.domains
Undergraduate courses: Multivariate Calculus, Ordinary Differential Equations, Theory of Probability, Discrete Probabilistic Methods, Linear Algebra, Financial Mathematics.
Large Deviations Techniques And Applications Amir Dembo
probability Amir Dembo and Ofer Zeitouni two of the leading researchers in the field provide an introduction to the theory of large deviations and applications at a level suitable for graduate …
Large Deviations Techniques And Applications Amir Dembo …
probability Amir Dembo and Ofer Zeitouni two of the leading researchers in the field provide an introduction to the theory of large deviations and applications at a level suitable for graduate …
Large Deviations Techniques And Applications Amir Dembo …
probability Amir Dembo and Ofer Zeitouni two of the leading researchers in the field provide an introduction to the theory of large deviations and applications at a level suitable for graduate …
Probability Theory: STAT310/MATH230 March 15, 2023
This chapter is devoted to the mathematical foundations of probability theory. Section 1.1 introduces the basic measure theory framework, namely, the probability space and the ˙ …
Stats 310A Session Notes - Yu Bai
This note contains Section materials for Stats 310A (Probability Theory I), Fall 2017 at Stanford University. Most of the materials follow the development of Dembo [2] and Billingsley [1].
Amir Dembo - Stanford University
ANNALS OF PROBABILITY Dembo, A., Peres, Y., Rosen, J. Model-free distributed learning. IEEE transactions on neural networks.
Title: Persistence Probabilities Amir Dembo, Stanford …
Amir Dembo, Stanford University . Persistence probabilities concern how likely it is that a stochastic . process has a long excursion above fixed level and of what are the . relevant...
Probability Theory: STAT310/MATH230 April15,2021
This chapter is devoted to the mathematical foundations of probability theory. Section 1.1 introduces the basic measure theory framework, namely, the probability space and the σ …
Gibbs Measures and Phase Transitions on Sparse Random …
Amir Dembo ∗, Andrea Montanari ∗ Stanford University. e-mail: amir@math.stanford.edu; montanari@stanford.edu Abstract: Many problems of interest in computer science and informa …
Homework 8 - Stanford University
Solve Exercises [3.3.10], [3.3.21], [3.3.23], in Amir Dembo’s lecture notes. An exercise on weak convergence of measures Let = f0;1gN be the set of (in nite) binary sequences != (! 1;! 2;! …
Large Deviations Techniques And Applications Amir Dembo …
probability Amir Dembo and Ofer Zeitouni two of the leading researchers in the field provide an introduction to the theory of large deviations and applications at a level suitable for graduate …
SPECTRAL MEASURE OF LARGE RANDOM HANKEL, MARKOV …
WLODZIMIERZˆ BRYC, AMIR DEMBO, AND TIEFENG JIANG Abstract. We study the limiting spectral measure of large symmetric random matrices of linear algebraic structure. For Hankel …
Midterm - web.stanford.edu
Let (Ω, F, P) be a probability space, denote by L2(Ω, F, P) the vector space of square integrable random variables. Given X1, . . . , Xn ∈ L2(Ω, F, P), let W({Xi}i∈[n]) be the vector space of …
MATH-60051 and MATH-70051 Probability Theory I Fall …
• Amir Dembo, Probability Theory • Varadhan, Probability Theory, (Ch. 1 – 3.6). Other books: • R.M. Dudley Real Analysis and Probability. Best account of the func-tional analysis and metric …
Probability Theory: STAT310/MATH230; September 12, 2010
This chapter is devoted to the mathematical foundations of probability theory. Section 1.1 introduces the basic measure theory framework, namely, the probability space and the ˙ …
Homework 7 - Stanford University
Solve Exercises [3.2.8], [3.2.9], [3.2.13], [3.2.26], [3.2.14] in Amir Dembo's lecture notes.
Practice Final - Stanford University
You can cite theorems (propositions, corollaries, lemmas, etc.) from Amir Dembo’s lecture notes by number, and exercises you have done as homework by number as well. Any other non …
Large Deviations Techniques And Applications Amir Dembo …
probability Amir Dembo and Ofer Zeitouni two of the leading researchers in the field provide an introduction to the theory of large deviations and applications at a level suitable for graduate …
Large Deviations Techniques And Applications Stochastic …
probability. Amir Dembo and Ofer Zeitouni, two of the leading researchers in the field, provide an introduction to the theory of large deviations and applications at a level suitable for graduate …
CURRICULUM VITAE - adembo.su.domains
Undergraduate courses: Multivariate Calculus, Ordinary Differential Equations, Theory of Probability, Discrete Probabilistic Methods, Linear Algebra, Financial Mathematics.
Large Deviations Techniques And Applications Amir Dembo
probability Amir Dembo and Ofer Zeitouni two of the leading researchers in the field provide an introduction to the theory of large deviations and applications at a level suitable for graduate …
Large Deviations Techniques And Applications Amir Dembo …
probability Amir Dembo and Ofer Zeitouni two of the leading researchers in the field provide an introduction to the theory of large deviations and applications at a level suitable for graduate …
Large Deviations Techniques And Applications Amir Dembo …
probability Amir Dembo and Ofer Zeitouni two of the leading researchers in the field provide an introduction to the theory of large deviations and applications at a level suitable for graduate …
