Modern Aspects of Random Matrix Theory (Google eBook)

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Van H. Vu
American Mathematical Society, Jul 16, 2014 - Mathematics - 176 pages
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The theory of random matrices is an amazingly rich topic in mathematics. Random matrices play a fundamental role in various areas such as statistics, mathematical physics, combinatorics, theoretical computer science, number theory and numerical analysis.

This volume is based on lectures delivered at the 2013 AMS Short Course on Random Matrices, held January 6-7, 2013 in San Diego, California.

Included are surveys by leading researchers in the field, written in introductory style, aiming to provide the reader a quick and intuitive overview of this fascinating and rapidly developing topic. These surveys contain many major recent developments, such as progress on universality conjectures, connections between random matrices and free probability, numerical algebra, combinatorics and high-dimensional geometry, together with several novel methods and a variety of open questions.

 

  

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Contents

Lecture notes on the circular law
1
Free probability and random matrices
35
Random matrix theory numerical computation and applications
53
Recent developments in nonasymptotic theory of random matrices
83
The universality phenomenon for Wigner ensembles
121
Back Cover
177
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