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Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 50,7 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814467995
Author : Édouard Brezin,Vladimir Kazakov,Didina Serban,Paul Wiegmann,Anton Zabrodin
Publisher : Springer Science & Business Media
Page : 519 pages
File Size : 50,9 Mb
Release : 2006-07-03
Category : Science
ISBN : 9781402045318
Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics. It can be useful to the specialists in various subjects using random matrices, from PhD students to confirmed scientists.
Author : Antonia M. Tulino,Sergio Verdú
Publisher : Now Publishers Inc
Page : 196 pages
File Size : 48,7 Mb
Release : 2004
Category : Computers
ISBN : 193301900X
Random Matrix Theory and Wireless Communications is the first tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained.
Author : Giacomo Livan,Marcel Novaes,Pierpaolo Vivo
Publisher : Springer
Page : 124 pages
File Size : 48,8 Mb
Release : 2018-01-16
Category : Science
ISBN : 9783319708850
Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum.The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory).Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.
Author : Pavel Bleher,Alexander Its
Publisher : Cambridge University Press
Page : 454 pages
File Size : 45,7 Mb
Release : 2001-06-04
Category : Mathematics
ISBN : 0521802091
Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.
Author : Marc Potters,Jean-Philippe Bouchaud
Publisher : Cambridge University Press
Page : 371 pages
File Size : 54,9 Mb
Release : 2020-12-03
Category : Computers
ISBN : 9781108488082
An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.
Author : Jinho Baik,Percy Deift,Toufic Suidan
Publisher : American Mathematical Soc.
Page : 461 pages
File Size : 55,8 Mb
Release : 2016-06-22
Category : Combinatorial analysis
ISBN : 9780821848418
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 : László Erdős,Horng-Tzer Yau
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 52,5 Mb
Release : 2017-08-30
Category : Random matrices
ISBN : 9781470436483
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 : Elizabeth S. Meckes
Publisher : Cambridge University Press
Page : 225 pages
File Size : 46,6 Mb
Release : 2019-08
Category : Mathematics
ISBN : 9781108419529
Provides a comprehensive introduction to the theory of random orthogonal, unitary, and symplectic matrices.
Author : Percy Deift,Dimitri Gioev
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 53,7 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9780821883570
"This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles-orthogonal, unitary, and symplectic. The authors follow the approach of Tracy and Widom, but the exposition here contains a substantial amount of additional material, in particular, facts from functional analysis and the theory of Pfaffians. The main result in the book is a proof of universality for orthogonal and symplectic ensembles corresponding to generalized Gaussian type weights following the authors' prior work. New, quantitative error estimates are derived." --Book Jacket.
Author : Gernot Akemann,Jinho Baik,Philippe Di Francesco
Publisher : Oxford Handbooks
Page : 0 pages
File Size : 54,8 Mb
Release : 2015-08-09
Category : Mathematics
ISBN : 0198744196
With a foreword by Freeman Dyson, the handbook brings together leading mathematicians and physicists to offer a comprehensive overview of random matrix theory, including a guide to new developments and the diverse range of applications of this approach.In part one, all modern and classical techniques of solving random matrix models are explored, including orthogonal polynomials, exact replicas or supersymmetry.
Author : Terence Tao
Publisher : American Mathematical Society
Page : 296 pages
File Size : 45,5 Mb
Release : 2023-08-24
Category : Mathematics
ISBN : 9781470474591
The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.
Author : Joel E. Cohen,Harry Kesten,Charles Michael Newman
Publisher : American Mathematical Soc.
Page : 358 pages
File Size : 46,5 Mb
Release : 1986
Category : Mathematics
ISBN : 9780821850442
These twenty-six expository papers on random matrices and products of random matrices survey the major results of the last thirty years. They reflect both theoretical and applied concerns in fields as diverse as computer science, probability theory, mathematical physics, and population biology. Many of the articles are tutorial, consisting of examples, sketches of proofs, and interpretations of results. They address a wide audience of mathematicians and scientists who have an elementary knowledge of probability theory and linear algebra, but not necessarily any prior exposure to this specialized area. More advanced articles, aimed at specialists in allied areas, survey current research with references to the original literature. The book's major topics include the computation and behavior under perturbation of Lyapunov exponents and the spectral theory of large random matrices. The applications to mathematical and physical sciences under consideration include computer image generation, card shuffling, and other random walks on groups, Markov chains in random environments, the random Schroedinger equations and random waves in random media. Most of the papers were originally presented at an AMS-IMS-SIAM Joint Summer Research Conference held at Bowdoin College in June, 1984. Of special note are the papers by Kotani on random Schroedinger equations, Yin and Bai on spectra for large random matrices, and Newman on the relations between the Lyapunov and eigenvalue spectra.
Author : Alexei Borodin,Ivan Corwin,Alice Guionnet
Publisher : American Mathematical Soc.
Page : 498 pages
File Size : 48,8 Mb
Release : 2019-10-30
Category : Education
ISBN : 9781470452803
Random matrix theory has many roots and many branches in mathematics, statistics, physics, computer science, data science, numerical analysis, biology, ecology, engineering, and operations research. This book provides a snippet of this vast domain of study, with a particular focus on the notations of universality and integrability. Universality shows that many systems behave the same way in their large scale limit, while integrability provides a route to describe the nature of those universal limits. Many of the ten contributed chapters address these themes, while others touch on applications of tools and results from random matrix theory. This book is appropriate for graduate students and researchers interested in learning techniques and results in random matrix theory from different perspectives and viewpoints. It also captures a moment in the evolution of the theory, when the previous decade brought major break-throughs, prompting exciting new directions of research.
Author : F. Mezzadri,N. C. Snaith
Publisher : Cambridge University Press
Page : 530 pages
File Size : 40,7 Mb
Release : 2005-06-21
Category : Mathematics
ISBN : 9780521620581
Provides a grounding in random matrix techniques applied to analytic number theory.
