Hardcover ISBN:  9781470452803 
Product Code:  PCMS/26 
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MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470454395 
Product Code:  PCMS/26.E 
List Price:  $112.00 
MAA Member Price:  $100.80 
AMS Member Price:  $89.60 
Hardcover ISBN:  9781470452803 
eBook: ISBN:  9781470454395 
Product Code:  PCMS/26.B 
List Price:  $237.00 $181.00 
MAA Member Price:  $213.30 $162.90 
AMS Member Price:  $189.60 $144.80 
Hardcover ISBN:  9781470452803 
Product Code:  PCMS/26 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470454395 
Product Code:  PCMS/26.E 
List Price:  $112.00 
MAA Member Price:  $100.80 
AMS Member Price:  $89.60 
Hardcover ISBN:  9781470452803 
eBook ISBN:  9781470454395 
Product Code:  PCMS/26.B 
List Price:  $237.00 $181.00 
MAA Member Price:  $213.30 $162.90 
AMS Member Price:  $189.60 $144.80 

Book DetailsIAS/Park City Mathematics SeriesVolume: 26; 2019; 498 ppMSC: Primary 15; 60; 82; 35; 46
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 breakthroughs, prompting exciting new directions of research.
Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute.
ReadershipGraduate students and researchers interested in random matrix theory and its many applications.

Table of Contents

Articles

Percy Deift — RiemannHilbert problems

Ioana Dumitriu — The semicircle law and beyond: The shape of spectra of Wigner matrices

László Erdős — The matrix Dyson equation and its applications for random matrices

Yan Fyodorov — Counting equilibria in complex systems via random matrices

Diane Holcomb and Bálint Virág — A short introduction to operator limits of random matrices

Jeremy Quastel and Konstantin Matetski — From the totally asymmetric simple exclusion process to the KPZ

Mark Rudelson — Delocalization of eigenvectors of random matrices

Sylvia Serfaty — Microscopic description of log and Coulomb gases

Dimitri Shlyakhtenko — Random matrices and free probability

Terence Tao — Least singular value, circular law, and Lindeberg exchange


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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 breakthroughs, prompting exciting new directions of research.
Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute.
Graduate students and researchers interested in random matrix theory and its many applications.

Articles

Percy Deift — RiemannHilbert problems

Ioana Dumitriu — The semicircle law and beyond: The shape of spectra of Wigner matrices

László Erdős — The matrix Dyson equation and its applications for random matrices

Yan Fyodorov — Counting equilibria in complex systems via random matrices

Diane Holcomb and Bálint Virág — A short introduction to operator limits of random matrices

Jeremy Quastel and Konstantin Matetski — From the totally asymmetric simple exclusion process to the KPZ

Mark Rudelson — Delocalization of eigenvectors of random matrices

Sylvia Serfaty — Microscopic description of log and Coulomb gases

Dimitri Shlyakhtenko — Random matrices and free probability

Terence Tao — Least singular value, circular law, and Lindeberg exchange