## Probability Seminar - Pei-Lun Tseng (Queen's University)

### Tuesday, April 3rd, 2018

**Time:** 3:30-5:00 p.m. **Place:** Jeffery Hall 319

**Speaker:** Pei-Lun Tseng (Queen's University)

**Title:** Linearization trick of infinitesimal freeness II

**Abstract: ** Last week, we introduced how to find a linearization for a given selfadjoint polynomial and showed some properties of this linearization. We will continue our discussion this week and introduce the operator-valued Cauchy transform. Then, we will show the algorithm for finding the distribution of $P$ where $P$ is a selfadjoint polynomial with selfadjoint variables $X$ and $Y$. Based on this method, we will discuss how to extend this algorithm for finding infinitesimal distribution for $P$.