Integrated density of states of the Anderson Hamiltonian with two-dimensional white noise

Abstract

We construct the integrated density of states of the Anderson Hamiltonian with two-dimensional white noise by proving the convergence of the Dirichlet eigenvalue counting measures associated with the Anderson Hamiltonians on the boxes. We also determine the logarithmic asymptotics of the left tail of the integrated density of states. Furthermore, we apply our result to a moment explosion of the parabolic Anderson model in the plane.

arXiv comment38 pages

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Cited by in corpus (3)

• Construction and spectrum of the Anderson Hamiltonian with white noise potential on ${\mathbf{R}}^2$ and ${\mathbf{R}}^3$
• Anderson Hamiltonians with singular potentials
• Asymptotic of the smallest eigenvalues of the continuous Anderson Hamiltonian in $d\le 3$