Transcription of An Introduction to Random Matrices
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An Introduction to Random Matrices
An Introduction to Random Matrices An Introduction to Random Matrices Greg W. Anderson University of Minnesota Alice Guionnet ENS Lyon Ofer Zeitouni University of Minnesota and Weizmann Institute of Science copyright information here To Meredith, Ben and Naomi Contents Preface page xiii 1 Introduction 1. 2 Real and Complex Wigner Matrices 6. Real Wigner Matrices : traces, moments and combinatorics 6. The semicircle distribution, Catalan numbers, and Dyck paths 7. Proof #1 of Wigner's Theorem 10. Proof of Lemma : Words and Graphs 11. Proof of Lemma : Sentences and Graphs 17. Some useful approximations 21. Maximal eigenvalues and Fu redi-Komlo s enumeration 23. Central limit theorems for moments 29.
This book is concerned with random matrices. Given the ubiquitous role that matrices play in mathematics and its application in the sciences and engineering, it seems natural that the evolution of probability theory would eventually pass through random matrices. The reality, however, has been more complicated (and interesting).
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