Random Matrix Theory And Its Applications: Multivariate Statistics And Wireless Communications

by Zhidong Bai, Yang Chen, Ying-chang Liang

Overview

Random matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparently random dispositions of the energy levels of heavy nuclei. The subject was further deeply developed under the important leadership of Dyson, Gaudin and Mehta, and other mathematical physicists.In the early 1990s, random matrix theory witnessed applications in string theory and deep connections with operator theory, and the integrable systems were established by Tracy and Widom. More recently, the subject has seen applications in such diverse areas as large dimensional data analysis and wireless communications.This volume contains chapters written by the leading participants in the field which will serve as a valuable introduction into this very exciting area of research.

Product Details

ISBN-13:	9789814273114
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	07/28/2009
Series:	Lecture Notes Series, Institute For Mathematical Sciences, National University Of Singapore , #18
Pages:	176
Product dimensions:	6.00(w) x 9.00(h) x 0.70(d)

Table of Contents

Foreword vii

Preface ix

The Stieltjes Transform and its Role in Eigenvalue Behavior of Large Dimensional Random Matrices Jack W. Silverstein 1

Beta Random Matrix Ensembles Peter J. Forrester 27

Future of Statistics Zhidong Bai Shurong Zheng 69

The η and Shannon Transforms: A Bridge between Random Matrices and Wireless Communications Antonia M. Tulino 95

The Replica Method in Multiuser Communications Ralf R. Müller 139