Publication list for Peres, Yuval

Publication list for Peres, Yuval

  • Zeros of Gaussian Analytic Functions and Determinantal Point Processes
    Base Product Code Keyword List: ulect; ULECT; ulect/51; ULECT/51; ulect-51; ULECT-51
    Print Product Code: ULECT/51
    Online Product Code: ULECT/51.E
    Title (HTML): Zeros of Gaussian Analytic Functions and Determinantal Point Processes
    Author(s) (Product display): J. Ben Hough; Manjunath Krishnapur; Yuval Peres; Bálint Virág
    Affiliation(s) (HTML): HBK Capital Management, New York, NY; Indian Institute of Science, Bangalore, India; Microsoft Research, Redmond, WA; University of Toronto, Toronto, ON, Canada
    Abstract:

    The book examines in some depth two important classes of point processes, determinantal processes and “Gaussian zeros”, i.e., zeros of random analytic functions with Gaussian coefficients. These processes share a property of “point-repulsion”, where distinct points are less likely to fall close to each other than in processes, such as the Poisson process, that arise from independent sampling. Nevertheless, the treatment in the book emphasizes the use of independence: for random power series, the independence of coefficients is key; for determinantal processes, the number of points in a domain is a sum of independent indicators, and this yields a satisfying explanation of the central limit theorem (CLT) for this point count. Another unifying theme of the book is invariance of considered point processes under natural transformation groups.

    The book strives for balance between general theory and concrete examples. On the one hand, it presents a primer on modern techniques on the interface of probability and analysis. On the other hand, a wealth of determinantal processes of intrinsic interest are analyzed; these arise from random spanning trees and eigenvalues of random matrices, as well as from special power series with determinantal zeros.

    The material in the book formed the basis of a graduate course given at the IAS-Park City Summer School in 2007; the only background knowledge assumed can be acquired in first-year graduate courses in analysis and probability.

    Book Series Name: University Lecture Series
    Volume: 51
    Publication Month and Year: 2009-10-13
    Copyright Year: 2009
    Page Count: 154
    Cover Type: Softcover
    Print ISBN-13: 978-0-8218-4373-4
    Online ISBN 13: 978-1-4704-1646-1
    Print ISSN: 1047-3998
    Online ISSN: 1047-3998
    Primary MSC: 60; 30; 15
    Textbook?: False
    Applied Math?: False
    Electronic Media?: False
    Apparel or Gift: False
    SXG Subject: PR; AN
    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/ulect-51
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    Readership:

    Graduate students and research mathematicians interested in random processes and their relations to complex analysis.

    Related Products: Markov Chains and Mixing Times
  • Markov Chains and Mixing Times: Second Edition
    Base Product Code Keyword List: mbk; MBK; mbk/107; MBK/107; mbk-107; MBK-107
    Print Product Code: MBK/107
    Online Product Code: MBK/107.E
    Title (HTML): Markov Chains and Mixing Times: Second Edition
    Author(s) (Product display): David A. Levin; Yuval Peres
    Affiliation(s) (HTML): University of Oregon, Eugene, OR; Microsoft Research, Redmond, WA
    Abstract:

    This book is an introduction to the modern theory of Markov chains, whose goal is to determine the rate of convergence to the stationary distribution, as a function of state space size and geometry. This topic has important connections to combinatorics, statistical physics, and theoretical computer science. Many of the techniques presented originate in these disciplines.

    The central tools for estimating convergence times, including coupling, strong stationary times, and spectral methods, are developed. The authors discuss many examples, including card shuffling and the Ising model, from statistical mechanics, and present the connection of random walks to electrical networks and apply it to estimate hitting and cover times.

    The first edition has been used in courses in mathematics and computer science departments of numerous universities. The second edition features three new chapters (on monotone chains, the exclusion process, and stationary times) and also includes smaller additions and corrections throughout. Updated notes at the end of each chapter inform the reader of recent research developments.

    Copyright Year: 2017
    Page Count: 447
    Cover Type: Hardcover
    Print ISBN-13: 978-1-4704-2962-1
    Online ISBN 13: 978-1-4704-4232-3
    Online ISSN:
    Primary MSC: 60; 65; 68; 82
    Textbook?: true
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    Home Page?: true
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    SXG Subject: PR
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    Print Outstock Reason: NYP
    Print Outstock Reason Avail Date: Expected publication date November 30, 2017
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    Print Add to Cart URL: /some/url/at/AMS/MBK-107
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    Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-4232-3&pisbn=978-1-4704-2962-1&epc=MBK/107.E&ppc=MBK/107&title=Markov%20Chains%20and%20Mixing%20Times%3A%20Second%20Edition&author=David%20A.%20Levin%3B%20Yuval%20Peres&type=R
    Readership:

    Undergraduate and graduate students interested in the modern theory of Markov chains.

    Reviews:

    Mixing times are an active research topic within many fields from statistical physics to the theory of algorithms, as well as having intrinsic interest within mathematical probability and exploiting discrete analogs of important geometry concepts. The first edition became an instant classic, being accessible to advanced undergraduates and yet bringing readers close to current research frontiers. This second edition adds chapters on monotone chains, the exclusion process and hitting time parameters. Having both exercises and citations to important research papers it makes an outstanding basis for either a lecture course or self-study.

    -- David Aldous, University of California, Berkeley

    Mixing time is the key to Markov chain Monte Carlo, the queen of approximation techniques. With new chapters on monotone chains, exclusion processes, and set-hitting, Markov Chains and Mixing Times is more comprehensive and thus more indispensable than ever. Prepare for an eye-opening mathematical tour!

    -- Peter Winkler, Dartmouth College

    The study of finite Markov chains has recently attracted increasing interest from a variety of researchers. This is the second edition of a very valuable book on the subject. The main focus is on the mixing time of Markov chains, but there is a lot of additional material.

    In this edition, the authors have taken the opportunity to add new material and bring the reader up to date on the latest research. I have used the first edition in a graduate course and I look forward to using this edition for the same purpose in the near future.

    -- Alan Frieze, Carnegie Mellon University

    Praise for the first edition:

    Markov Chains and Mixing Times is a magical book, managing to be both friendly and deep. It gently introduces probabilistic techniques so that an outsider can follow. At the same time, it is the first book covering the geometric theory of Markov chains and has much that will be new to experts. It is certainly THE book that I will use to teach from. I recommend it to all comers, an amazing achievement.

    -- Persi Diaconis, Mary V. Sunseri Professor of Statistics and Mathematics, Stanford University

    In this book, [the authors] rapidly take a well-prepared undergraduate to the frontiers of research. Short, focused chapters with clear logical dependencies allow readers to use the book in multiple ways.

    -- CHOICE Magazine

    Related Products: Markov Chains and Mixing Times Knowing the Odds
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  • Markov Chains and Mixing Times
    Base Product Code Keyword List: mbk; MBK; mbk/58; MBK/58; mbk-58; MBK-58
    Print Product Code: MBK/58
    Online Product Code: MBK/58.E
    Title (HTML): Markov Chains and Mixing Times
    Author(s) (Product display): David A. Levin; Yuval Peres; Elizabeth L. Wilmer
    Affiliation(s) (HTML): University of Oregon, Eugene, OR; Microsoft Research, Redmond, WA and University of Washington, Seattle, WA and University of California, Berkeley, Berkeley, CA; Oberlin College, Oberlin, OH
    Abstract:

    This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of random walks on networks, including hitting and cover times, and analyses of several methods of shuffling cards. As a prerequisite, the authors assume a modest understanding of probability theory and linear algebra at an undergraduate level. Markov Chains and Mixing Times is meant to bring the excitement of this active area of research to a wide audience.

    Publication Month and Year: 2008-12-09
    Copyright Year: 2009
    Page Count: 371
    Cover Type: Hardcover
    Print ISBN-13: 978-0-8218-4739-8
    Online ISBN 13: 978-1-4704-1204-3
    Primary MSC: 60; 65; 68; 82
    Textbook?: true
    Applied Math?: false
    Electronic Media?: false
    Apparel or Gift: false
    SXG Subject: PR
    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/mbk-58
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    Readership:

    Undergraduates, graduate students, and research mathematicians interested in probability, combinatorics, simulation, computer science, and Markov chain.

    Reviews:

    Markov Chains and Mixing Times is a magical book, managing to be both friendly and deep. It gently introduces probabilistic techniques so that an outsider can follow. At the same time, it is the first book covering the geometric theory of Markov chains and has much that will be new to experts. It is certainly THE book that I will use to teach from. I recommend it to all comers, an amazing achievement.

    -- Persi Diaconis, Mary V. Sunseri Professor of Statistics and Mathematics, Stanford University

    A superb introduction to Markov chains which treats riffle shuffling and stationary times...

    -- Sami Assaf, University of Southern California, Persi Diaconis, Stanford University, and Kannan Soundararajan, Stanford University, in their paper "Riffle Shuffles with Biased Cuts"

    In this book, [the authors] rapidly take a well-prepared undergraduate to the frontiers of research. Short, focused chapters with clear logical dependencies allow readers to use the book in multiple ways.

    -- CHOICE Magazine

    This book is a beautiful introduction to Markov chains and the analysis of their convergence towards a stationary distribution. Personally, I enjoyed very much the lucid and clear writing style of the exposition in combination with full mathematical rigor and the fascinating relations of the theory of Markov chains to several other mathematical areas.

    -- Zentralblatt MATH

    Throughout the book, the authors generously provide concrete examples that motivate theory and illustrate ideas. I expect this superb book to be widely used in graduate courses around the world, and to become a standard reference.

    -- Mathematical Reviews

    Related Products: Zeros of Gaussian Analytic Functions and Determinantal Point Processes
  • Game Theory, Alive
    Base Product Code Keyword List: mbk; MBK; mbk/101; MBK/101; mbk-101; MBK-101
    Print Product Code: MBK/101
    Online Product Code: MBK/101.E
    Title (HTML): Game Theory, Alive
    Author(s) (Product display): Anna R. Karlin; Yuval Peres
    Affiliation(s) (HTML): University of Washington, Seattle, WA; Microsoft Research, Redmond, WA
    Abstract:

    We live in a highly connected world with multiple self-interested agents interacting and myriad opportunities for conflict and cooperation. The goal of game theory is to understand these opportunities.

    This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science (algorithmic game theory), economics (auctions and matching markets), social choice (voting theory), biology (signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments.

    The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, or statistics. The importance of game-theoretic thinking transcends the academic setting—for every action we take, we must consider not only its direct effects, but also how it influences the incentives of others.

    Publication Month and Year: 2017-04-27
    Copyright Year: 2017
    Page Count: 372
    Cover Type: Hardcover
    Print ISBN-13: 978-1-4704-1982-0
    Online ISBN 13: 978-1-4704-3667-4
    Online ISSN:
    Primary MSC: 91
    Textbook?: true
    Applied Math?: true
    Home Page?: false
    Sample?: false
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    Apparel or Gift: false
    SXG Subject: DM; AP
    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/mbk-101
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    Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-3667-4&pisbn=978-1-4704-1982-0&epc=MBK/101.E&ppc=MBK/101&title=Game%20Theory%2C%20Alive&author=Anna%20R.%20Karlin%3B%20Yuval%20Peres&type=R
    Readership:

    Undergraduate and graduate students and professors interested in game theory and decision making.

    Reviews:

    This is an attractive candidate as a text for a mathematically rigorous course in game theory at the upper undergraduate or elementary graduate level. It offers an appealing and versatile selection of topics (including some modern ones), clear and well-motivated exposition, a good selection of examples, and a nicely-chosen selection of exercises (some but not all of which have solutions in the back of the book). People who teach, or simply have an interest in game theory, will certainly find this book worth a look.

    -- Mark Hunacek, MAA Reviews

    Game theory's influence is felt in a wide range of disciplines, and the authors deliver masterfully on the challenge of presenting both the breadth and coherence of its underlying world-view. The book achieves a remarkable synthesis, introducing the reader to the blend of economic insight, mathematical elegance, scientific impact, and counter-intuitive punch that characterizes game theory as a field.

    -- Jon Kleinberg, Cornell University, 2006 Nevanlinna Prize winner

    A game theory textbook by people who love … games! It covers many classic as well as recent topics of game theory. Its rigorous treatment, interspersed with illuminating examples, makes it a challenging pleasure to read.

    -- Sergiu Hart, The Hebrew University of Jerusalem

    This beautifully written book introduces the reader to the rich and flourishing subject of game theory. From an exhaustive account of basics of the classical theory to a wide range of modern themes—including auctions, matching markets, sequential decision making—the book presents a great variety of topics in a rigorous yet entertaining manner. The authors guide the reader through the intricacies of game theory with an exquisite mathematical elegance. For anyone interested in the topic, experts and beginners alike, this book is a must.

    -- Gábor Lugosi, Pompeu Fabra University, Barcelona, Spain

    It is great to have a comprehensive game theory textbook including so many modern topics.

    -- Éva Tardos, Cornell University

    Related Products: Combinatorial Game Theory An Introductory Course on Mathematical Game Theory Markov Chains and Mixing Times
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  • A Power Law of Order 1/4 for Critical Mean Field Swendsen-Wang Dynamics
    Base Product Code Keyword List: memo; MEMO; memo/232; MEMO/232; memo-232; MEMO-232; memo/232/1092; MEMO/232/1092; memo-232-1092; MEMO-232-1092
    Print Product Code: MEMO/232/1092
    Online Product Code: MEMO/232/1092.E
    Title (HTML): A Power Law of Order 1/4 for Critical Mean Field Swendsen-Wang Dynamics
    Author(s) (Product display): Yun Long; Asaf Nachmias; Weiyang Ning; Yuval Peres
    Affiliation(s) (HTML): University of California, Berkeley; University of British Columbia, Vancouver, British Columbia, Canada; University of Washington, Seattle, Washington; Microsoft Research, Redmond, Washington
    Abstract:

    The Swendsen-Wang dynamics is a Markov chain widely used by physicists to sample from the Boltzmann-Gibbs distribution of the Ising model. Cooper, Dyer, Frieze and Rue proved that on the complete graph \(K_n\) the mixing time of the chain is at most \(O(\sqrt{n})\) for all non-critical temperatures.

    In this paper the authors show that the mixing time is \(\Theta(1)\) in high temperatures, \(\Theta(\log n)\) in low temperatures and \(\Theta(n^{1/4})\) at criticality. They also provide an upper bound of \(O(\log n)\) for Swendsen-Wang dynamics for the \(q\)-state ferromagnetic Potts model on any tree of \(n\) vertices.

    Book Series Name: Memoirs of the American Mathematical Society
    Publication Month and Year: 2014-09-29
    Copyright Year: 2014
    Page Count: 84
    Cover Type: Softcover
    Print ISBN-13: 978-1-4704-0910-4
    Online ISBN 13: 978-1-4704-1895-3
    Print ISSN: 0065-9266
    Online ISSN: 0065-9266
    Primary MSC: 60
    Secondary MSC: 82
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    SXG Subject: PR
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