Moment Methods on compact groups: Weingarten calculus and its applications
Operator Algebras
2024-05-10 v1 Mathematical Physics
math.MP
Probability
Abstract
A fundamental property of compact groups and compact quantum groups is the existence and uniqueness of a left and right invariant probability -- the Haar measure. This is a natural playground for classical and quantum probability, provided it is possible to compute its moments. Weingarten calculus addresses this question in a systematic way. The purpose of this manuscript is to survey recent developments, describe some salient theoretical properties of Weingarten functions, as well as applications of this calculus to random matrix theory, quantum probability, and algebra, mathematical physics and operator algebras.
Keywords
Cite
@article{arxiv.2207.08418,
title = {Moment Methods on compact groups: Weingarten calculus and its applications},
author = {Benoit Collins},
journal= {arXiv preprint arXiv:2207.08418},
year = {2024}
}
Comments
20 pages, contribution to the ICM 2022, sections Analysis and Probability