论文标题
紧凑型组的力矩方法：Weingarten演算及其应用
Moment Methods on compact groups: Weingarten calculus and its applications
论文作者
论文摘要
紧凑型组和紧凑型量子组的基本特性是左右不变概率的存在和独特性 - HAAR度量。只要有可能计算其时刻，这是古典和量子概率的自然游乐场。 Weingarten微积分以系统的方式解决了这个问题。本手稿的目的是调查最近的发展，描述Weingarten函数的某些显着理论特性，以及该积分对随机基质理论，量子概率和代数，数学物理和操作员代数的应用。
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.
