Research Seminar Noncommutative and Functional Analysis

Next Talk

Date: 11.07.2022
Speaker: Marwa Banna (NYU Abu Dhabi)

Title: Berry-Esseen Bounds for Operator-valued Free Limit Theorems

Abstract:
The development of free probability theory has drawn much inspiration from its deep and far reaching analogy with classical probability theory. The same holds for its operator-valued extension, where the fundamental notion of free independence is generalized to free independence with amalgamation as a kind of conditional version of the former. Its development naturally led to operator-valued free analogues of key and fundamental limiting theorems such as the operator-valued free Central Limit Theorem due to Voiculescu and the asymptotic distributions of matrices with operator-valued entries.

In this talk, we show Berry-Esseen bounds for such limit theorems. The estimates are on the level of operator-valued Cauchy transforms and the L\'evy distance. We also address the multivariate setting for which we consider linear matrix pencils and noncommutative polynomials as test functions. The estimates are in terms of operator-valued moments and yield the first quantitative bounds on the Lévy distance for the operator-valued free CLT. This also yields quantitative estimates on joint noncommutative distributions of operator-valued matrices having a general covariance profile.

This is a joint work with Tobias Mai.

Time and Place

Mondays 16 c.t. in HS IV, E 2.4

For the list of upcoming and past talks see this link.