- Covers a variety of different facets of free probability, giving a flavor of the breadth of the subject
- Features exercises scattered throughout the text
- Showcases basic ideas and results in order to focus on their relation
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- Über dieses Buch
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This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory.
The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
- Stimmen zum Buch
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“This book is an excellent survey, respectively introduction, into recent developments in free probability theory and its applications to random matrices. The authors superbly guide the reader through a number of important examples and present a carefully selected list of 207 relevant publications.” (Ludwig Paditz, zbMATH 1387.60005, 2018)
- Inhaltsverzeichnis (12 Kapitel)
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Asymptotic Freeness of Gaussian Random Matrices
Seiten 1-21
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The Free Central Limit Theorem and Free Cumulants
Seiten 23-49
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Free Harmonic Analysis
Seiten 51-91
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Asymptotic Freeness for Gaussian, Wigner, and Unitary Random Matrices
Seiten 93-120
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Fluctuations and Second Order Freeness
Seiten 121-158
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Inhaltsverzeichnis (12 Kapitel)
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Bibliografische Information
- Bibliographic Information
-
- Buchtitel
- Free Probability and Random Matrices
- Autoren
-
- James A. Mingo
- Roland Speicher
- Titel der Buchreihe
- Fields Institute Monographs
- Buchreihen Band
- 35
- Copyright
- 2017
- Verlag
- Springer-Verlag New York
- Copyright Inhaber
- Springer Science+Business Media LLC
- eBook ISBN
- 978-1-4939-6942-5
- DOI
- 10.1007/978-1-4939-6942-5
- Hardcover ISBN
- 978-1-4939-6941-8
- Softcover ISBN
- 978-1-4939-8346-9
- Buchreihen ISSN
- 1069-5273
- Auflage
- 1
- Seitenzahl
- XIV, 336
- Anzahl der Bilder
- 45 schwarz-weiß Abbildungen
- Themen
