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arXiv · 1907.01352

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

Khalil Chouk·Willem van Zuijlen
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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 $L\rightarrow \infty$ almost surely to the same deterministic constant, which is given by a variational formula.

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Khalil Chouk, Willem van Zuijlen. 2019-07-02. Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions. https://doi.org/10.1214/20-aop1497

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