Outline:

1. This is an introductory course in Free Probability Theory, a branch in operator theory and operator algebra. We will discuss random matrix theory and the connection between classical and free probability. Only a knowledge of (real) functional analysis and probability theory is required for this course.

Objective:

We will begin with free product in free probability, and then talk about RMT.

Textbook:

1. Z. Bai and J. W. Silverstein, Spectral Analysis of Large Dimensional Random Matrices
2. R. Couillet and M. Debbah, Random Matrix Methods for Wireless Communications
3. F. Hiai and D. Petz, The Semicircle Law, Free Random Variables, and Entropy
4. A. Nica and R. Speicher, Lectures on the combinatorics of free probability
5. T. Tao, Topics in random matri Theory
6. D. V. Voiculescu, K. J. Dykema, A. Nica, Free Random Variables