Description

Book Synopsis


Trade Review
“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)

Table of 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.

Free Probability and Random Matrices 35 Fields

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    A Hardback by James A. Mingo, Roland Speicher

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      Book details

      Publisher Springer Nature
      Published 26 June 2017
      ISBN-13 9781493969418
      978-1493969418
      ISBN-10 1493969412
      Also in:
      Functional analysis and transforms Stochastics

      Description

      Book Synopsis


      Trade Review
      “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)

      Table of 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.

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