Free probability and random matrices

• 作者： Mingo, James A., author.
• 其他作者：
  • Speicher, Roland, author.
  • SpringerLink (Online service)
• 其他題名：
  • Fields institute monographs ;
• 出版： New York, NY : Springer New York :Imprint: Springer
• 叢書名： Fields institute monographs,volume 35
• 主題： Free probability theory. , Random matrices. , Mathematics. , Probability Theory and Stochastic Processes. , Functional Analysis.
• ISBN： 9781493969425 (electronic bk.) 、 9781493969418 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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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• 摘要註: 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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