Log-gases and random matrices
Author(s)
Bibliographic Information
Log-gases and random matrices
（London Mathematical Society monograph series, v. 34）
Princeton University Press, c2010
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Note
Includes bibliographical references (p. [765]-784) and index
Description and Table of Contents
Description
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; Painleve 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.
Table of Contents
*FrontMatter, pg. i*Preface, pg. v*Contents, pg. xi*Chapter One. Gaussian Matrix Ensembles, pg. 1*Chapter Two. Circular Ensembles, pg. 53*Chapter Three. Laguerre And Jacobi Ensembles, pg. 85*Chapter Four. The Selberg Integral, pg. 133*Chapter Five. Correlation functions at ss = 2, pg. 186*Chapter Six. Correlation Functions At ss= 1 And 4, pg. 236*Chapter Seven. Scaled limits at ss = 1, 2 and 4, pg. 283*Chapter Eight. Eigenvalue probabilities - Painleve systems approach, pg. 328*Chapter Nine. Eigenvalue probabilities- Fredholm determinant approach, pg. 380*Chapter Ten. Lattice paths and growth models, pg. 440*Chapter Eleven. The Calogero-Sutherland model, pg. 505*Chapter Twelve. Jack polynomials, pg. 543*Chapter Thirteen. Correlations for general ss, pg. 592*Chapter Fourteen. Fluctuation formulas and universal behavior of correlations, pg. 658*Chapter Fifteen. The two-dimensional one-component plasma, pg. 701*Bibliography, pg. 765*Index, pg. 785
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