Weyl law for the Anderson Hamiltonian on a two-dimensional manifold
Analysis of PDEs
2021-07-09 v4 Mathematical Physics
math.MP
Probability
Spectral Theory
Abstract
We define the Anderson Hamiltonian H on a two-dimensional manifold using high order paracontrolled calculus. It is a self-adjoint operator with pure point spectrum. We get lower and upper bounds on its eigenvalues which imply an almost sure Weyl-type law for H.
Keywords
Cite
@article{arxiv.2009.03549,
title = {Weyl law for the Anderson Hamiltonian on a two-dimensional manifold},
author = {Antoine Mouzard},
journal= {arXiv preprint arXiv:2009.03549},
year = {2021}
}