Free Probability and Random Matrices / by James A. Mingo, Roland Speicher

By:

Mingo, James A [aut]

Contributor(s):

Speicher, Roland, 1960- [oth]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Fields Institute Monographs ; 35 | SpringerLink BücherPublisher: New York, NY : Springer, 2017Publisher: [Erscheinungsort nicht ermittelbar] : The Fields Institute for Research in the Mathematical Sciences, 2017Description: Online-Ressource (XIV, 336 p. 45 illus, online resource)ISBN:

9781493969425

Subject(s):

Additional physical formats: 9781493969418 | Druckausg.: 978-1-4939-6941-8 | Erscheint auch als: Free probability and random matrices. Druck-Ausgabe New York, NY : Springer, 2017. xiv, 336 SeitenDDC classification:

519.2

MSC: MSC: *60-02 | 60F05 | 60F10 | 60G15 | 15B52 | 60B20RVK: RVK: SK 860LOC classification:

QA273.A1-274.9 QA274-274.9
QA273.A1-274.9
QA274-274.9

DOI: DOI: 10.1007/978-1-4939-6942-5Online resources:

Summary: 1. Asymptotic Freeness of Gaussian Random Matrices -- 2. The Free Central Limit Theorem and Free Cumulants -- 3. Free Harmonic Analysis -- 4. Asymptotic Freeness -- 5. Second Order Freeness -- 6. Free Group Factors and Freeness -- 7. Free Entropy X-the Microstates Approach via Large Deviations -- Free Entropy X*-the Non-Microstates Approach via Free Fisher Information -- 9. Operator-Valued Free Probability Theory and Block Random Matrices -- 10. Polynomials in Free Variables and Operator-Valued Convolution -- 11. Brown Measure -- Solutions to Exercises -- References -- Index of ExercisesSummary: 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 physicsPPN: PPN: 1659300037Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA

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