Random matrices
著者
書誌事項
Random matrices
（IAS/Park City mathematics series / [Dan Freed, series editor], v. 26）
American Mathematical Society, c2019
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注記
"Institute for Advanced Study"
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
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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