Log-Gases and Random Matrices (Lms-34)

Peter J Forrester

ISBN 10: 0691128294 / ISBN 13: 9780691128290

Editore: Princeton University Press Jul 2010, 2010

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Neuware - 'Encyclopedic in scope, this book achieves an excellent balance between the theoretical and physical approaches to the subject. It coherently leads the reader from first-principle definitions, through a combination of physical and mathematical arguments, to the full derivation of many fundamental results. The vast amount of material and impeccable choice of topics make it an invaluable reference.'--Eduardo Dueñez, University of Texas, San Antonio.

Codice articolo 9780691128290

Dati bibliografici

• Titolo: Log-Gases and Random Matrices (Lms-34)
• Editore: Princeton University Press Jul 2010
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 0691128294
• ISBN 13: 9780691128290
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 261 L x 211 A x 43 P (millimetri) 261 millimetri di larghezza per 211 millimetri di altezza per 43 millimetri di profondità
• Peso: 1751 grammi

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

Peter J. Forrester is professor of mathematics at the University of Melbourne.