TY - BOOK ID - 77880614 TI - Log-gases and random matrices PY - 2010 SN - 1282641743 9786612641749 1400835410 9781400835416 9780691128290 0691128294 PB - Princeton (N.J.): Princeton university press, DB - UniCat KW - Random matrices. KW - Jacobi polynomials. KW - Integral theorems. KW - Theorems, Integral KW - Integrals KW - Polynomials, Jacobi KW - Orthogonal polynomials KW - Matrices, Random KW - Matrices KW - Integral theorems KW - Jacobi polynomials KW - Random matrices KW - 519.218 KW - 519.218 Special stochastic processes KW - Special stochastic processes UR - https://www.unicat.be/uniCat?func=search&query=sysid:77880614 AB - 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. ER -