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Free Probability and Random Matrices [electronic resource] / by James A. Mingo, Roland Speicher.

By: Contributor(s): Material type: TextTextSeries: Fields Institute Monographs ; 35Publisher: New York, NY : Springer New York : Imprint: Springer, 2017Description: XIV, 336 p. 45 illus. online resourceContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781493969425
Subject(s): Additional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification:
  • 519.2 23
LOC classification:
  • QA273.A1-274.9
  • QA274-274.9
Online resources:
Contents:
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.
In: Springer eBooksSummary: 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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Holdings
Item type Current library Call number Status Date due Barcode Item holds
E-BOOKS ISI Library, Kolkata Not for loan EB1963
Total holds: 0

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.

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