Free Probability and Random Matrices

• Main Authors: Mingo, James A. (Author), Speicher, Roland (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2017.
• Series: Fields Institute Monographs, 35
• Subjects: Mathematics.; Functional analysis.; Probabilities.; Probability Theory and Stochastic Processes.; Functional Analysis.

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...

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.