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Free probability and random matrices

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Free probability and random matrices/ by James A. Mingo, Roland Speicher.
Author:	Mingo, James A.
other author:	Speicher, Roland.
Published:	New York, NY :Springer New York : : 2017.,
Description:	xiv, 336 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Free probability theory. -
Online resource:	http://dx.doi.org/10.1007/978-1-4939-6942-5
ISBN:	9781493969425

Free probability and random matrices
Mingo, James A.

Free probability and random matrices[electronic resource] /by James A. Mingo, Roland Speicher. - New York, NY :Springer New York :2017. - xiv, 336 p. :ill., digital ;24 cm. - Fields institute monographs,v.351069-5273 ;. - Fields institute monographs ;v.34..

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 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.

ISBN: 9781493969425

Standard No.: 10.1007/978-1-4939-6942-5doiSubjects--Topical Terms:

1173205
Free probability theory.

LC Class. No.: QA326

Dewey Class. No.: 512.55

Free probability and random matrices
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505 0 $a 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.
520 $a 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.
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