ランダム行列の理論と応用 Random Matrix Theory and Its Applications: Multivariate Statistics and Wireless Communications (Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore)

Bai, Zhidong (EDT)/ Chen, Yang (EDT)/ Liang, Ying-chang (EDT)

World Scientific Publishing Co Pte Ltd（2009/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 176 p.
• 言語 ENG
• 商品コード 9789814273114
• DDC分類 519.2

Full Description

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.

Contents

The Stieltjes Transform and Its Role in Eigenvalue Behavior of Large Dimensional Random Matrices (J W Silverstein); Beta Random Matrix Ensembles (P Forrester); Future of Statistics (Z Bai);  and Shannon Transforms: A Bridge between Random Matrices and Wireless Communications (A M Tulino); The Replica Method in Multiuser Communications (R R Muller).