WIAS Preprint No. 2606, (2019)

Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimension



Authors

  • Chouk, Khalil
  • van Zuijlen, Willem

2010 Mathematics Subject Classification

  • 60H25 60F15 35J10 35P15 60F10

Keywords

  • Anderson Hamiltonian, white noise, paracontrolled distributions, operators with Dirichlet boundary, conditions

DOI

10.20347/WIAS.PREPRINT.2606

Abstract

In this paper we consider the Anderson Hamiltonian with white noise potential on the box [0,L]² with Dirichlet boundary conditions. We show that all the eigenvalues divided by log L converge as L → ∞ almost surely to the same deterministic constant, which is given by a variational formula.

Download Documents