Moment methods on compact groups: Weingarten calculus and its applications

DOI DOI オープンアクセス

説明

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.

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

収録刊行物

関連プロジェクト

もっと見る

キーワード

詳細情報 詳細情報について

問題の指摘

ページトップへ