Free probability and random matrices / James A. Mingo, Roland Speicher.
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 gro...
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Main Authors: | , |
Format: | eBook |
Language: | English |
Published: |
New York :
Springer,
[2017]
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Series: | Fields Institute monographs ;
35. |
Subjects: |
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.