Title	Asymptotic freeness of Biane-Perelemov-Popov matrices
Creator	Novak, Jonathan
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2016-12-06T13:59
Description	Biane-Perelemov-Popov matrices are a family of quantum random matrices which quantize uniformly random Hermitian matrices with deterministic eigenvalues and uniformly random eigenvectors. BPP matrices depend on a semiclassical parameter which controls the degree of noncommutativity of their entries. Improving on results of Biane and Collins-Sniady, and resolving a conjecture of Bufetov-Gorin, we demonstrate that classically independent BPP matrices become asymptotically free provided the semiclassical parameter decays as the dimension increases. This result has consequences in asymptotic representation theory, implying in particular that $GL_N(\mathbb{C})$ tensor products are described by free probability in any and all semiclassical limits. This is joint work with Collins and Sniady.
Extent	54 minutes
Subject	Mathematics; Functional analysis; Probability theory and stochastic processes; Operator theory/algebras
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: University of California, San Diego
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2017-05-15
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0347460
URI	http://hdl.handle.net/2429/61629
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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Asymptotic freeness of Biane-Perelemov-Popov matrices Novak, Jonathan

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