The random matrix theory of the classical compact groups / Elizabeth S. Meckes.

Format:

Book

Author/Creator:

Meckes, Elizabeth S., author.

Series:

Cambridge tracts in mathematics ; 218.

Cambridge tracts in mathematics ; 218

Language:

English

Subjects (All):

Random matrices.

Matrices.

Physical Description:

1 online resource (xi, 212 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2019.

Summary:

This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.

Contents:

The classification and the first main theorem

NC-groups

The B-NB classification

NB-Groups

Other classes of locally compact groups

The geometric theory. An introduction

The geometric NC-theorem

Algebra and geometries on C-groups

The end game in the C-theorem

The metric classification

The homotopy and homology classification of connected Lie groups

The polynomial homology for simply connected soluble groups

Cohomology on Lie groups.

Notes:

Title from publisher's bibliographic system (viewed on 05 Jul 2019).

Includes bibliographical references and index.

ISBN:

1-108-31799-5

1-108-32171-2

1-108-30345-5