The book treats free probability theory, which has been extensively developed since the early 1980s. The emphasis is put on entropy and the random matrix model approach. The volume 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 the book is the parallelism between the normal and semicircle laws. Voiculescu’s multivariate free entropy theory is presented with full proofs and extends the results to unitary operators. Some applications to operator algebras are also given. Based on lectures given by the authors in Hungary, Japan, and Italy, the book is a good reference for mathematicians interested in free probability theory and can serve as a text for an advanced graduate course.
Fumio Hiai
Semicircle Law, Free Random Variables and Entropy [PDF ebook]
Semicircle Law, Free Random Variables and Entropy [PDF ebook]
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Formato PDF ● Pagine 376 ● ISBN 9781470413040 ● Casa editrice American Mathematical Society ● Scaricabile 3 volte ● Moneta EUR ● ID 6613580 ● Protezione dalla copia Adobe DRM
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