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Author: Percy Deift
Publisher: Cambridge University Press
Published: 2014-12-15
Total Pages: 539
ISBN-13: 1107079926
DOWNLOAD EBOOK →This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.
Author: John Harnad
Publisher: Springer Science & Business Media
Published: 2011-05-06
Total Pages: 536
ISBN-13: 1441995145
DOWNLOAD EBOOK →This book explores the remarkable connections between two domains that, a priori, seem unrelated: Random matrices (together with associated random processes) and integrable systems. The relations between random matrix models and the theory of classical integrable systems have long been studied. These appear mainly in the deformation theory, when parameters characterizing the measures or the domain of localization of the eigenvalues are varied. The resulting differential equations determining the partition function and correlation functions are, remarkably, of the same type as certain equations appearing in the theory of integrable systems. They may be analyzed effectively through methods based upon the Riemann-Hilbert problem of analytic function theory and by related approaches to the study of nonlinear asymptotics in the large N limit. Associated with studies of matrix models are certain stochastic processes, the "Dyson processes", and their continuum diffusion limits, which govern the spectrum in random matrix ensembles, and may also be studied by related methods. Random Matrices, Random Processes and Integrable Systems provides an in-depth examination of random matrices with applications over a vast variety of domains, including multivariate statistics, random growth models, and many others. Leaders in the field apply the theory of integrable systems to the solution of fundamental problems in random systems and processes using an interdisciplinary approach that sheds new light on a dynamic topic of current research.
Author: Richard Durrett
Publisher: American Mathematical Soc.
Published: 1985
Total Pages: 394
ISBN-13: 0821850423
DOWNLOAD EBOOK →Covers the proceedings of the 1984 AMS Summer Research Conference. This work provides a summary of results from some of the areas in probability theory; interacting particle systems, percolation, random media (bulk properties and hydrodynamics), the Ising model and large deviations.
Author: Jinho Baik
Publisher: American Mathematical Soc.
Published: 2016-06-22
Total Pages: 461
ISBN-13: 0821848410
DOWNLOAD EBOOK →Over the last fifteen years a variety of problems in combinatorics have been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a “stochastic special function theory” for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.
Author: Jinho Baik
Publisher: American Mathematical Soc.
Published: 2008-01-01
Total Pages: 452
ISBN-13: 9780821857861
DOWNLOAD EBOOK →Of special interest is the article of Percy Deift in which he discusses some open problems of Random Matrix Theory und the theory of integrable systems."--BOOK JACKET.
Author: Pavel Bleher
Publisher: Cambridge University Press
Published: 2001-06-04
Total Pages: 454
ISBN-13: 9780521802093
DOWNLOAD EBOOK →Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.
Author: László Erdős
Publisher: American Mathematical Soc.
Published: 2017-08-30
Total Pages: 226
ISBN-13: 1470436485
DOWNLOAD EBOOK →A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Author: T.M. Liggett
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 499
ISBN-13: 1461385423
DOWNLOAD EBOOK →At what point in the development of a new field should a book be written about it? This question is seldom easy to answer. In the case of interacting particle systems, important progress continues to be made at a substantial pace. A number of problems which are nearly as old as the subject itself remain open, and new problem areas continue to arise and develop. Thus one might argue that the time is not yet ripe for a book on this subject. On the other hand, this field is now about fifteen years old. Many important of several basic models is problems have been solved and the analysis almost complete. The papers written on this subject number in the hundreds. It has become increasingly difficult for newcomers to master the proliferating literature, and for workers in allied areas to make effective use of it. Thus I have concluded that this is an appropriate time to pause and take stock of the progress made to date. It is my hope that this book will not only provide a useful account of much of this progress, but that it will also help stimulate the future vigorous development of this field.
Author: Marc Potters
Publisher: Cambridge University Press
Published: 2020-12-03
Total Pages: 371
ISBN-13: 1108488080
DOWNLOAD EBOOK →An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.
Author: Elizabeth S. Meckes
Publisher: Cambridge University Press
Published: 2019-08-01
Total Pages: 225
ISBN-13: 1108317995
DOWNLOAD EBOOK →This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.
