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Chouk, Khalil [Author]; van Zuijlen, Willem [Author]

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

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  • Media type: Text; Report; E-Book
  • Title: Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions
  • Contributor: Chouk, Khalil [Author]; van Zuijlen, Willem [Author]
  • Published: Weierstrass Institute for Applied Analysis and Stochastics publication server, 2019
  • Language: English
  • DOI: https://doi.org/10.20347/WIAS.PREPRINT.2606
  • Keywords: 35J10 ; 60F15 ; 60F10 ; 60H25 ; Anderson Hamiltonian -- white noise -- paracontrolled distributions -- operators with Dirichlet boundary -- conditions ; 35P15 ; article
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  • Description: 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.