A dynamical approach to random matrix theory

Author(s)

• Erdős, László
• Yau, Horng-Tzer

Bibliographic Information

A dynamical approach to random matrix theory

László Erdős, Horng-Tzer Yau

（Courant lecture notes in mathematics, 28）

Courant Institute of Mathematical Sciences, New York University , American Mathematical Society, c2017

• : [pbk.]

Note

Includes bibliographical references (p. 217-223) and index

Description and Table of Contents

Description

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.

Table of Contents

Introduction Wigner matrices and their generalizations Eigenvalue density Invariant ensembles Universality for generalized Wigner matrices Local semicircle law for universal Wigner matrices Weak local semicircle law Proof of the local semicircle law Sketch of the proof of the local semicircle law using the spectral gap Fluctuation averaging mechanism Eigenvalue location: The rigidity phenomenon Universality for matrices with Gaussian convolutions Entropy and the logarithmic Sobolev inequality (LSI) Universality of the Dyson Brownian motion Continuity of local correlation functions under the matrix OU process Universality of Wigner matrices in small energy windows: GFT Edge universality Further results and historical notes References Index

by "Nielsen BookData"

Details

• NCID: BB24459018
• ISBN:
  • 9781470436483
• LCCN: 2017012815
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: New York,Providence, R.I.
• Pages/Volumes: ix, 226 p.
• Size: 26 cm
• Classification:
  • LCC : QA196.5
  • DC23 : 512.9/434
• Subject Headings:
  • LCSH : Random matrices
• Parent Bibliography ID:
  • BA42224256