Moment methods on compact groups: Weingarten calculus and its applications (Q6119189)
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scientific article; zbMATH DE number 7822649
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Moment methods on compact groups: Weingarten calculus and its applications |
scientific article; zbMATH DE number 7822649 |
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Moment methods on compact groups: Weingarten calculus and its applications (English)
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22 March 2024
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Summary: 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 very natural playground for classical and quantum probability, provided that 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. For the entire collection see [Zbl 07816358].
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Haar measure on compact groups
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Weingarten calculus
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asymptotic freeness
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quantum information theory
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quantum groups
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Schur-Weyl duality
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norm estimates
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random tensors
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