Free Probability and Random Matrices

1. Asymptotic Freeness of Gaussian Random Matrices
James A. Mingo, Roland Speicher

2. The Free Central Limit Theorem and Free Cumulants
James A. Mingo, Roland Speicher

3. Free Harmonic Analysis
James A. Mingo, Roland Speicher

4. Asymptotic Freeness for Gaussian, Wigner, and Unitary Random Matrices
James A. Mingo, Roland Speicher

5. Fluctuations and Second Order Freeness
James A. Mingo, Roland Speicher

6. Free Group Factors and Freeness
James A. Mingo, Roland Speicher

7. Free Entropy χ: The Microstates Approach via Large Deviations
James A. Mingo, Roland Speicher

8. Free Entropy χ
∗: The Non-microstates Approach via Free Fisher Information
James A. Mingo, Roland Speicher

9. Operator-Valued Free Probability Theory and Block Random Matrices
James A. Mingo, Roland Speicher

10. Deterministic Equivalents, Polynomials in Free Variables, and Analytic Theory of Operator-Valued Convolution
James A. Mingo, Roland Speicher

11. Brown Measure
James A. Mingo, Roland Speicher

12. Solutions to Exercises
James A. Mingo, Roland Speicher

Avainsanat: Mathematics, Probability Theory and Stochastic Processes, Functional Analysis