Anderson Hamiltonians with singular potentials
Probability
2026-05-14 v3 Spectral Theory
Abstract
We construct random Schr\"odinger operators, called Anderson Hamiltonians, with Dirichlet and Neumann boundary conditions for a fairly general class of singular random potentials on bounded domains. Furthermore, we construct the integrated density of states of these Anderson Hamiltonians, and we relate the Lifschitz tails (the asymptotics of the left tails of the integrated density of states) to the left tails of the principal eigenvalues.
Cite
@article{arxiv.2211.01199,
title = {Anderson Hamiltonians with singular potentials},
author = {Toyomu Matsuda and Willem van Zuijlen},
journal= {arXiv preprint arXiv:2211.01199},
year = {2026}
}
Comments
The main text contains 50 pages. The appendices contain 32 pages. Reorganisation and relocation of some text: most notably on the main assumptions: see the introduction, beginning Section 1.4 and Section 1.5; and Section 3