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BIMSA-Tsinghua Quantum Symmetry Seminar
Upgrading free convolution to non-normal random variables
Upgrading free convolution to non-normal random variables
Organizers
Speaker
Ping Zhong
Time
Wednesday, March 20, 2024 10:30 AM - 12:00 PM
Venue
A3-3-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
The free probability theory is a probability theory of noncommutative random variables, where usual independence isreplaced by free independence. It was initially designed to study longstanding problems about von Neumann algebras of freegroups. It turns out to be an extremely powerful framework to study the universality laws in random matrix theory due to thegroundbreaking work of Voiculescu. These limiting laws are encoded in abstract operators. called free random variables.
Brown measure is a sort of spectral measure for free random variables. not necessarily normal, I will report some recentprogress on the Brown measure of the sum $X + Y$ of two free random variables $X$ and $Y$, where $Y$ has certain symmetryor explicit $R$-transform. The procedure relies on Hermitian reduction and subordination functions. The Brown measure resultscan predict the limit eigenvalue distribution of various full rank deformed random matrix models. The talk is based on mywork on Brown measure of elliptic operators and ioint works with Hari Bercovici. Serban Belinschi and Zhi Yin