- Date: 27 Apr. (Thu.)
- Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
- Time: 16:30 – 18:00
- Speaker: Katsunori Fujie (Hokkaido University)
- Title: Combinatorial approach to finite free probability

Abstract: Since the 2010s, when Marcus, Spielman, and Srivastava solved the Kadison–Singer conjecture and found a connection between its solution and free probability theory, this research area has been called finite free probability.

Much progress has been made recently, and of particular interest are finite free cumulants by Octavio and Perales, where free cumulants are the basic tool used as a discretization for the characteristic function in the context of free probability.

Just recently, the speaker, Octavio Arizmendi (CIMAT) and Yuki Ueda (Hokkaido Education University) have proved a few limit theorems in finite free probability by a unified approach using finite free cumulants in arXiv:2303.01790.

The purpose of this talk is to introduce our approach.

After a brief description of the field, we will explain the combinatorial formulas that are key to the solution.

Then, as an application, we will present the limit theorems in finite free probability and their correspondence with free probability theory.