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Log-gases and random matrices
"Random matrix theory, both as an application and as theory, has evolved rapidly over the past fifteen years. [This book] 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 po...
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| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Log-gases and random matrices / P. J. Forrester |
| Publié : |
Princeton (N. J.), Oxford :
Princeton University Press
, cop. 2010 |
| Description matérielle : | 1 vol. (XIV-791 p.) |
| Collection : | London Mathematical Society monographs series editors Martin Bridson, Terry Lyons, Peter Sarnak,... ; 34 |
| Contenu : | Contient des exercices |
| Sujets : |
| Résumé : | "Random matrix theory, both as an application and as theory, has evolved rapidly over the past fifteen years. [This book] 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 developche ment 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 multiple 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 formuls ; nonintersecting paths and models in statistical mechanisms ; and applications of random matrix theory. This is the first textbook development of both non-symmetric and symmetric Jack polynomial theory, as well as the connection between Selberg integral theory and beta ensembles." (source : 4ème de couverture) |
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| Bibliographie : | Bibliogr. p. [765]-784. Index |
| ISBN : | 978-0-691-12829-0 0-691-12829-4 |