Overview

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.

Full Product Details

Author:   Alexei Borodin ,  Ivan Corwin ,  Alice Guionnet
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   1.100kg
ISBN:  

9781470452803

ISBN 10:   1470452804
Pages:   508
Publication Date:   30 January 2020
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

P. Deift, Riemann-Hilbert problems I. Dumitriu, The semicircle law and beyond: The shape of spectra of Wigner matrices L. Erdos, The matrix Dyson equation and its applications for random matrices Y. V. Fyodorov, Counting equilibria in complex systems via random matrices D. Holcomb and B. Virag, A short introduction to operator limits of random matrices J. Quastel and K. Matetski, From the totally asymmetric simple exclusion process to the KPZ M. Rudelson, Delocalization of eigenvectors of random matrices S. Serfaty, Microscopic description of log and Coulomb gases D. Shlyakhtenko, Random matrices and free probability T. Tao, Least singular value, circular law, and Lindeberg exchange.

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Author Information

Alexei Borodin, Massachusetts Institute of Technology, Cambridge, MA. Ivan Corwin, Columbia University, New York, NY. Alice Guionnet, CNRS, ENS Lyon, France.

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