Non UBC
DSpace
Constanze Liaw
2019-09-30T08:37:50Z
2019-04-02T16:34
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.
https://circle.library.ubc.ca/rest/handle/2429/71802?expand=metadata
33.0 minutes
video/mp4
Author affiliation: Delaware
Banff (Alta.)
10.14288/1.0381038
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Researcher
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Operator theory
Group theory and generalizations
Functional analysis
Rank-one perturbations and Anderson-type Hamiltonians
Moving Image
http://hdl.handle.net/2429/71802