# Student Probability Seminar

#### Sums of Noncommuting Random Variables and Free Harmonic Analysis

**Speaker:**
Ben McKenna

**Location:**
Warren Weaver Hall 805

**Date:**
Thursday, March 8, 2018, 11 a.m.

**Synopsis:**

*What is the distribution of the sum of two random variables? The independent case is classical and fully understood; the distribution is a convolution, and as such can be computed using harmonic analysis. We will answer this question when the random variables are noncommutative. We'll see how to define a``free convolution,'' and explain how this can be computed with the Stieltjes transform (which is of related interest in its own right as a fundamental link between complex analysis and random matrix theory). Our motivating example throughout will be simple random walk on the free group F_d on d letters, and specifically how recurrence/transience depend on d - the noncommutative analogue of Polya's classical theorem on Z^d.*

**Notes:**

No knowledge of free probability will be assumed.