arXiv:2207.08418 Abstract | arXiv Analytics

arXiv:2207.08418 [math.OA]Abstract References Reviews Resources

Moment Methods on compact groups: Weingarten calculus and its applications

Published 2022-07-18Version 1

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.

Comments: 20 pages, contribution to the ICM 2022, sections Analysis and Probability

Categories: math.OA, math-ph, math.MP, math.PR

Subjects: 28C10, 15B52, 60B20

Keywords: compact groups, moment methods, applications, quantum probability, compact quantum groups

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