Learning Seminar in Random Matrices and Free Probability  

This is a learning seminar for free probability and related topics. We meet in Sid Richardson 344 2:30-3:30 pm Wednesdays. 

Schedule 2025

• Feb. 7 Lp decomposition of free group algebras (by Tao Mei)

• Jan. 21     Lp boundedness of smooth Schur multipliers (by Jose Conde )

Schedule 2024

• Nov. 6 Haagerup tensor product and products for operator systems (by Adam Dor-On and Travis Russell)

• Oct. 9.       Lp decompositon of free groups (by Sheng Yin)

• Sept. 11    Maximal functions on BMO (by Dauitbek Dostilek)

• May. 1st     Lusemberg problem for noncommutative Measures (by Dauitbek Dostilek)

• Apr. 24 X_p inequalities  (by Ismael Cano)

• Apr. 17 Zeros of polynomials and finite free probability (by Andrei Martínez-Finkelshtein)

• Apr. 10 Zeros of polynomials and finite free probability (by Andrei Martínez-Finkelshtein)

• Apr. 3 Algebraicity of Cauchy transforms (by Sheng Yin)

• Mar. 27 Algebraicity of Cauchy transforms (by Sheng Yin)

• Mar. 20 Cauchy transforms and noncommutative formal power series (by Javier Parcet, ICMAT Spain)

• Feb. 28 Structure of free group factors (by Zhiyuan Yang (TAMU))

• Feb. 21 Lp spaces on free groups (by Tao Mei)

• Feb. 14 Lp spaces on free groups (by Edward Mcdonald (PenState ))

• Feb. 7 Basics on free groups (by Tao Mei)

Schedule 2023

• May 3 Convergence of rational functions in random matrices (by Sheng Yin)

• Apr. 26    Concentration inequality for GOE (by Zhenchuan Liu)

• Apr. 19    Semicircular law of GOE (by Sheng Yin)

• Apr. 12    R-transform of the free convolution of probability measures with finite variance [3] (by Sheng Yin)

• Apr. 5       Characterization of positive definite, radial functions on free groups (by Chian Yeong Chuah)

• Mar. 29   R-transforms of probability measures with finite variance (cont.) [3] (by Sheng Yin)

• Mar. 22   R-transforms of probability measures with finite variance [3] (by Sheng Yin)

• Mar. 8      Examples of R-transforms (by Sheng Yin)

• Mar. 1      Free cumulants (by Daniel Perales)

• Feb. 22    R-transforms of compactly supported measures [3] (by Sheng Yin)

• Feb. 15    Cauchy transforms (cont.) [3] (by Sheng Yin)

• Feb. 8       Cauchy transforms [3] (by Sheng Yin)

Schedule 2022

• Oct. 26    Uniqueness of the tensor product and free product [5] (by Sheng Yin)

• Oct. 19    Universal products of noncommutative probability spaces [5] (by Sheng Yin)

• Oct. 12    q-Gaussian random variables and q-Hermite polynomials [2] (by Sheng Yin)

• Sep. 28    q-Fock spaces [1] (by Sheng Yin)

• Sep. 21    Realization of free semicircular random variables (by Sheng Yin)

• Sep. 14    Fock spaces (by Sheng Yin)

References

1.  M. Bożejko, R. Speicher. An example of a generalized Brownian motion, Comm Math Phys, 137, 519–531, 1991.

2.  M. Bożejko, B. Kümmerer and R. Speicher, q-Gaussian Processes: Non-commutative and Classical Aspects, Comm Math Phys 185, 129–154, 1997.

3.  J. Mingo, R. Speicher, Free Probability and Random Matrices. Fields Institute Monographs, Vol. 35, Springer, New York, 2017.

4. A. Nica, R. Speicher, Lectures on the Combinatorics of Free Probability, Cambridge University Press, 2006.

5. R. Speicher, On universal products. In Free probabilty theory (Waterloo, ON, 1995), volume 12 of Fields Inst. Commun., pages 257—266. Amer. Math. Soc., Providence, RI, 1997.