The Oxford Handbook of Random Matrix Theory

The Oxford Handbook of Random Matrix Theory
Title The Oxford Handbook of Random Matrix Theory PDF eBook
Author Gernot Akemann
Publisher Oxford Handbooks
Pages 0
Release 2015-08-09
Genre Mathematics
ISBN 9780198744191

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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.

The Oxford Handbook of Random Matrix Theory

The Oxford Handbook of Random Matrix Theory
Title The Oxford Handbook of Random Matrix Theory PDF eBook
Author Gernot Akemann
Publisher OUP Oxford
Pages 0
Release 2011-07-28
Genre Mathematics
ISBN 9780199574001

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Random matrix theory is applied by physicists and mathematicians to understand phenomena in nature and deep mathematical structures. This book offers a comprehensive look at random matrix theory by leading researchers, including applications inside and outside of physics and mathematics.

Introduction to Random Matrices

Introduction to Random Matrices
Title Introduction to Random Matrices PDF eBook
Author Giacomo Livan
Publisher Springer
Pages 122
Release 2018-01-16
Genre Science
ISBN 3319708856

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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.

A Dynamical Approach to Random Matrix Theory

A Dynamical Approach to Random Matrix Theory
Title A Dynamical Approach to Random Matrix Theory PDF eBook
Author László Erdős
Publisher American Mathematical Soc.
Pages 239
Release 2017-08-30
Genre Mathematics
ISBN 1470436485

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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.

Combinatorics and Random Matrix Theory

Combinatorics and Random Matrix Theory
Title Combinatorics and Random Matrix Theory PDF eBook
Author Jinho Baik
Publisher American Mathematical Soc.
Pages 478
Release 2016-06-22
Genre Mathematics
ISBN 0821848410

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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.

A First Course in Random Matrix Theory

A First Course in Random Matrix Theory
Title A First Course in Random Matrix Theory PDF eBook
Author Marc Potters
Publisher Cambridge University Press
Pages 371
Release 2020-12-03
Genre Computers
ISBN 1108488080

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An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.

Random Matrix Theory

Random Matrix Theory
Title Random Matrix Theory PDF eBook
Author Percy Deift
Publisher American Mathematical Soc.
Pages 236
Release 2009-01-01
Genre Mathematics
ISBN 0821883577

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"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.