Title	Rank-one perturbations and Anderson-type Hamiltonians
Creator	Liaw, Constanze
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2019-04-02T16:34
Description	A rank-one perturbation $A+K$ of an operator $A$ is one where the range of $K$ is just one-dimensional. Being rather restrictive, they form a small class of perturbations. Yet, rank-one perturbations are related to many deep questions. Here we focus on a relation with Anderson-type Hamiltonians. These are random perturbations which are obtained by taking a countable sum of rank-one perturbation, each weighted by a randomly chosen coupling constant. Such perturbations are non-compact almost surely. Under mild conditions, the essential parts of two realizations of an Anderson-type Hamiltonian are almost surely related by a rank one perturbation.
Extent	33.0 minutes
Subject	Mathematics; Operator theory; Group theory and generalizations; Functional analysis
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Delaware
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2019-09-30
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0381038
URI	http://hdl.handle.net/2429/71802
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Researcher
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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