WIAS Preprint No. 2976, (2022)

Anderson Hamiltonians with singular potentials


Authors

  • Matsuda, Toyomu
  • van Zuijlen, Willem
    ORCID: 0000-0002-2079-0359

2020 Mathematics Subject Classification

  • 60H17 60H25 60L40 82B44 35J10 35P15

Keywords

  • Anderson Hamiltonian, regularity structures, integrated density of states

DOI

10.20347/WIAS.PREPRINT.2976

Abstract

We construct random Schrödinger operators, called Anderson Hamiltonians, with Dirichlet and Neumann boundary conditions for a fairly general class of singular random potentials on bounded domains. Furthermore, we construct the integrated density of states of these Anderson Hamiltonians, and we relate the Lifschitz tails (the asymptotics of the left tails of the integrated density of states) to the left tails of the principal eigenvalues.

Download Documents