Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions
- Chouk, Khalil
- van Zuijlen, Willem
2010 Mathematics Subject Classification
- 60H25 60F15 35J10 35P15 60F10
- Anderson Hamiltonian, white noise, paracontrolled distributions, operators with Dirichlet boundary, conditions
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.
- Ann. Probab., 49 (2021), pp. 1917--1964, DOI 10.1214/20-AOP1497 .