Free Probability and Random Matrices

James A. Mingo, Roland Speicher (Autoren)

Buch | Softcover

336 Seiten

2018 | Softcover reprint of the original 1st ed. 2017
Springer-Verlag New York Inc.
978-1-4939-8346-9 (ISBN)

Artikel merken

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.

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 Exercises.

“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)

Erscheinungsdatum	16.08.2018
Reihe/Serie	Fields Institute Monographs ; 35
Zusatzinfo	45 Illustrations, black and white; XIV, 336 p. 45 illus.
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	asymptotic freeness • Cauchy transform • free central limit theorem • free harmonic analysis • Guassian random matrices
ISBN-10	1-4939-8346-6 / 1493983466
ISBN-13	978-1-4939-8346-9 / 9781493983469
Zustand	Neuware