Log-gases and random matrices / P.J. Forrester.

Format:

Book

Author/Creator:

Forrester, Peter (Peter John)

Series:

London Mathematical Society monographs.

London Mathematical Society monographs

Language:

English

Subjects (All):

Random matrices.

Jacobi polynomials.

Integral theorems.

Physical Description:

1 online resource (806 p.)

Edition:

Course Book

Place of Publication:

Princeton : Princeton University Press, c2010.

Language Note:

English

Summary:

Random matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. Log-Gases and Random Matrices gives a comprehensive account of these developments, emphasizing log-gases as a physical picture and heuristic, as well as covering topics such as beta ensembles and Jack polynomials. Peter Forrester presents an encyclopedic development of log-gases and random matrices viewed as examples of integrable or exactly solvable systems. Forrester develops not only the application and theory of Gaussian and circular ensembles of classical random matrix theory, but also of the Laguerre and Jacobi ensembles, and their beta extensions. Prominence is given to the computation of a multitude of Jacobians; determinantal point processes and orthogonal polynomials of one variable; the Selberg integral, Jack polynomials, and generalized hypergeometric functions; Painlevé transcendents; macroscopic electrostatistics and asymptotic formulas; nonintersecting paths and models in statistical mechanics; and applications of random matrix theory. This is the first textbook development of both nonsymmetric and symmetric Jack polynomial theory, as well as the connection between Selberg integral theory and beta ensembles. The author provides hundreds of guided exercises and linked topics, making Log-Gases and Random Matrices an indispensable reference work, as well as a learning resource for all students and researchers in the field.

Contents:

Frontmatter

Preface

Contents

Chapter One. Gaussian Matrix Ensembles

Chapter Two. Circular Ensembles

Chapter Three. Laguerre And Jacobi Ensembles

Chapter Four. The Selberg Integral

Chapter Five. Correlation functions at β = 2

Chapter Six. Correlation Functions At β= 1 And 4

Chapter Seven. Scaled limits at β = 1, 2 and 4

Chapter Eight. Eigenvalue probabilities - Painlevé systems approach

Chapter Nine. Eigenvalue probabilities- Fredholm determinant approach

Chapter Ten. Lattice paths and growth models

Chapter Eleven. The Calogero-Sutherland model

Chapter Twelve. Jack polynomials

Chapter Thirteen. Correlations for general β

Chapter Fourteen. Fluctuation formulas and universal behavior of correlations

Chapter Fifteen. The two-dimensional one-component plasma

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786612641749

9781282641747

1282641743

9781400835416

1400835410

OCLC:

656260887