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The Semicircle Law, Free Random Variables And Entropy

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This text 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 presentation demonstrates 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.

Language: English

Pages: 386

Format: Hardcover

Publisher: American Mathematical Society(RI)

Release: January 01, 2000

ISBN: 0821820818

ISBN 13: 9780821820810

The Semicircle Law, Free Random Variables And Entropy

0/5 ( ratings)

This text 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 presentation demonstrates 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.

Language: English

Pages: 386

Format: Hardcover

Publisher: American Mathematical Society(RI)

Release: January 01, 2000

ISBN: 0821820818

ISBN 13: 9780821820810

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