The Semicircle Law, Free Random Variables, and Entropy: No. 77 - Rilegato

Hiai, Fumio; Petz, Denes

Rilegato

ISBN 10: 0821820818 ISBN 13: 9780821820810

Casa editrice: Amer Mathematical Society, 2000

Riassunto

The book treats free probability theory, which has been extensively developed since the early eighties. The emphasis is put on entropy and the random matrix model approach. It is a unique presentation demonstrating the extensive interrelation between the topics. Wigner's theorem and its broad generalizations, such as asymptotic freeness of independent matrices, are explained in detail. Consistent throughout is the parallelism between the normal and semicircle laws. The authors present Voiculescu's multivariate free entropy theory with full proofs and extend the results to unitary operators. Some applications to operator algebras are also given. The book is the first essentially full-scale presentation on free probability theory and includes improvements of results and proofs in current literature. The combinatorial aspects of the specialized topics are emphasized; many examples are given. The book would be a suitable text for graduate courses in free probability theory.

Dettagli dell?edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2000
• Lingua: Inglese
• ISBN 10: 0821820818
• ISBN 13: 9780821820810
• Rilegatura: Copertina rigida
• Numero di pagine: 376
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile