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

### Tuesday, March 27th, 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

**Abstract: ** For given infinitesimal distribution of selfadjoint elements $X$, $Y$, and given a selfadjoint polynomial $P$ with variable $X$ and $Y$. The natural question is whether we can write down the precise formula for the infinitesimal distribution of $P$? In 2009 Belinschi and Shlyakhtenko gave a precise formula to solve for the infinitesimal distribution of $P$ for $P(X,Y)=X+Y$. In the talk, we will discuss how to find the formula for an arbitrary polynomial by using the linearization trick.