The Library
On spatial conditioning of the spectrum of discrete Random Schrödinger operators
Tools
Tools
Tools
Gaudreau Lamarre, Pierre Yves, Ghosal, Promit and Liao, Yuchen (2022) On spatial conditioning of the spectrum of discrete Random Schrödinger operators. Journal of Spectral Theory, 12 (3). pp. 1109-1153. doi:10.4171/jst/415 ISSN 1664-039X.
|
PDF
10362042-10.4171-jst-415-print.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (442Kb) | Preview |
Official URL: https://doi.org/10.4171/jst/415
Abstract
Consider a random Schrödinger-type operator of the form H WD HX C V C � acting on a general graph G D .V; E/, where HX is the generator of a Markov process X on G, V is a deterministic potential with sufficient growth (so that H has a purely discrete spectrum), and � is a random noise with at-most-exponential tails. We prove that the eigenvalue point
process of H is number rigid in the sense of Ghosh and Peres (2017); that is, the number of eigenvalues in any bounded domain B � C is determined by the configuration of eigenvalues outside of B. Our general setting allows to treat cases where X could be non-symmetric (hence
H is non-self-adjoint) and � has long-range dependence. Our strategy of proof consists of controlling the variance of the trace of the semigroup etH using the Feynman–Kac formul
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| SWORD Depositor: | Library Publications Router | ||||||
| Library of Congress Subject Headings (LCSH): | Schrödinger operator, Spectral theory (Mathematics), Random operators | ||||||
| Journal or Publication Title: | Journal of Spectral Theory | ||||||
| Publisher: | European Mathematical Society - EMS - Publishing House GmbH | ||||||
| ISSN: | 1664-039X | ||||||
| Official Date: | 22 April 2022 | ||||||
| Dates: |
|
||||||
| Volume: | 12 | ||||||
| Number: | 3 | ||||||
| Page Range: | pp. 1109-1153 | ||||||
| DOI: | 10.4171/jst/415 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | ** From Crossref journal articles via Jisc Publications Router ** History: epub 21-04-2023; issued 21-04-2023. | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Date of first compliant deposit: | 14 June 2023 | ||||||
| Date of first compliant Open Access: | 14 June 2023 |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
