Ground state energy of trimmed discrete Schrödinger operators and localization for trimmed Anderson models
Alexander Elgart
Virginia Tech, Blacksburg, USAAbel Klein
University of California, Irvine, USA
![Ground state energy of trimmed discrete Schrödinger operators and localization for trimmed Anderson models cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jst-volume-4-issue-2.png&w=3840&q=90)
Abstract
We consider discrete Schrödinger operators of the form on , where is the discrete Laplacian and is a bounded potential. Given , the -trimming of is the restriction of to , denoted by . We investigate the dependence of the ground state energy on . We show that for relatively dense proper subsets of we always have . We use this lifting of the ground state energy to establish Wegner estimates and localization at the bottom of the spectrum for -trimmed Anderson models, i.e., Anderson models with the random potential supported by the set .
Cite this article
Alexander Elgart, Abel Klein, Ground state energy of trimmed discrete Schrödinger operators and localization for trimmed Anderson models. J. Spectr. Theory 4 (2014), no. 2, pp. 391–413
DOI 10.4171/JST/74