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.
