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.

A Dynamical Approach to Random Matrix Theory (Courant Lecture Notes) (Courant Lecture Notes inn Mathematics)

Science & Math

Laszlo Erdos

Horng-Tzer Yau

Mathematics

American Mathematical Society

Based on lectures held at the Center for Theoretical Sciences in Taiwan in honor of Louis Nirenberg’s 75th birthday, the volume contains both research papers dealing with various problems in Partial Differential Equations such as wave maps, the Navier-Stokes equations, and Lagrangian submanifolds. 
Professor Nirenberg is particularly appreciated for his generous encouragement of the development of mathematics in the Asia-Pacific region and the mixture of articles by distinguished mathematicians from Asia and other parts of the world.

Lectures on Partial Differential Equations: Proceedings in honor of Louis Nirenberg's 75th Birthday

Sun-Yung Alice Chang

Chang-Shou Lin

International Press of Boston

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