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Author :
Publisher :
ISBN 13 : 9782856298503
Total Pages : pages
Book Rating : 4.2/5 (985 download)
Download or read book Advanced Topics in Random Matrices written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Terence Tao
Publisher : American Mathematical Society
ISBN 13 : 147047459X
Total Pages : 296 pages
Book Rating : 4.4/5 (74 download)
Download or read book Topics in Random Matrix Theory written by Terence Tao and published by American Mathematical Society. This book was released on 2023-08-24 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Greg W. Anderson
Publisher : Cambridge University Press
ISBN 13 : 0521194520
Total Pages : 507 pages
Book Rating : 4.5/5 (211 download)
Download or read book An Introduction to Random Matrices written by Greg W. Anderson and published by Cambridge University Press. This book was released on 2010 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.
Author : Giacomo Livan
Publisher : Springer
ISBN 13 : 3319708856
Total Pages : 124 pages
Book Rating : 4.3/5 (197 download)
Download or read book Introduction to Random Matrices written by Giacomo Livan and published by Springer. This book was released on 2018-01-16 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : László Erdős
Publisher : American Mathematical Soc.
ISBN 13 : 1470436485
Total Pages : 226 pages
Book Rating : 4.4/5 (74 download)
Download or read book A Dynamical Approach to Random Matrix Theory written by László Erdős and published by American Mathematical Soc.. This book was released on 2017-08-30 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Percy Deift
Publisher : American Mathematical Soc.
ISBN 13 : 0821883577
Total Pages : 236 pages
Book Rating : 4.8/5 (218 download)
Download or read book Random Matrix Theory written by Percy Deift and published by American Mathematical Soc.. This book was released on 2009-01-01 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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 : Alexei Borodin
Publisher : American Mathematical Soc.
ISBN 13 : 1470452804
Total Pages : 498 pages
Book Rating : 4.4/5 (74 download)
Download or read book Random Matrices written by Alexei Borodin and published by American Mathematical Soc.. This book was released on 2019-10-30 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 0821874306
Total Pages : 298 pages
Book Rating : 4.8/5 (218 download)
Download or read book Topics in Random Matrix Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2012-03-21 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Peter J. Forrester
Publisher : Princeton University Press
ISBN 13 : 1400835410
Total Pages : 808 pages
Book Rating : 4.4/5 (8 download)
Download or read book Log-Gases and Random Matrices (LMS-34) written by Peter J. Forrester and published by Princeton University Press. This book was released on 2010-07-01 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. Log-Gases and Random Matrices gives a comprehensive account of these developments, emphasizing log-gases as a physical picture and heuristic, as well as covering topics such as beta ensembles and Jack polynomials. Peter Forrester presents an encyclopedic development of log-gases and random matrices viewed as examples of integrable or exactly solvable systems. Forrester develops not only the application and theory of Gaussian and circular ensembles of classical random matrix theory, but also of the Laguerre and Jacobi ensembles, and their beta extensions. Prominence is given to the computation of a multitude of Jacobians; determinantal point processes and orthogonal polynomials of one variable; the Selberg integral, Jack polynomials, and generalized hypergeometric functions; Painlevé transcendents; macroscopic electrostatistics and asymptotic formulas; nonintersecting paths and models in statistical mechanics; and applications of random matrix theory. This is the first textbook development of both nonsymmetric and symmetric Jack polynomial theory, as well as the connection between Selberg integral theory and beta ensembles. The author provides hundreds of guided exercises and linked topics, making Log-Gases and Random Matrices an indispensable reference work, as well as a learning resource for all students and researchers in the field.
Author : Jinho Baik
Publisher : American Mathematical Soc.
ISBN 13 : 0821848410
Total Pages : 461 pages
Book Rating : 4.8/5 (218 download)
Download or read book Combinatorics and Random Matrix Theory written by Jinho Baik and published by American Mathematical Soc.. This book was released on 2016-06-22 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Leonid Andreevich Pastur
Publisher : American Mathematical Soc.
ISBN 13 : 082185285X
Total Pages : 650 pages
Book Rating : 4.8/5 (218 download)
Download or read book Eigenvalue Distribution of Large Random Matrices written by Leonid Andreevich Pastur and published by American Mathematical Soc.. This book was released on 2011 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries). The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes. This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.
Author : Marc Potters
Publisher : Cambridge University Press
ISBN 13 : 1108488080
Total Pages : 371 pages
Book Rating : 4.1/5 (84 download)
Download or read book A First Course in Random Matrix Theory written by Marc Potters and published by Cambridge University Press. This book was released on 2020-12-03 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 1108317995
Total Pages : 225 pages
Book Rating : 4.1/5 (83 download)
Download or read book The Random Matrix Theory of the Classical Compact Groups written by Elizabeth S. Meckes and published by Cambridge University Press. This book was released on 2019-08-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Joel E. Cohen
Publisher : American Mathematical Soc.
ISBN 13 : 082185044X
Total Pages : 376 pages
Book Rating : 4.8/5 (218 download)
Download or read book Random Matrices and Their Applications written by Joel E. Cohen and published by American Mathematical Soc.. This book was released on 1986 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features twenty-six expository papers on random matrices and products of random matrices. This work reflects both theoretical and applied concerns in fields as diverse as computer science, probability theory, mathematical physics, and population biology.
Author : Gernot Akemann
Publisher : Oxford Handbooks
ISBN 13 : 9780198744191
Total Pages : 0 pages
Book Rating : 4.7/5 (441 download)
Download or read book The Oxford Handbook of Random Matrix Theory written by Gernot Akemann and published by Oxford Handbooks. This book was released on 2015-08-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)
Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author : James A. Mingo
Publisher : Springer
ISBN 13 : 1493969420
Total Pages : 336 pages
Book Rating : 4.4/5 (939 download)
Download or read book Free Probability and Random Matrices written by James A. Mingo and published by Springer. This book was released on 2017-06-24 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
