Ground state energy of trimmed discrete Schrödinger operators and localization for trimmed Anderson models

  • Alexander Elgart

    Virginia Tech, Blacksburg, USA
  • Abel Klein

    University of California, Irvine, USA

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