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arXiv · 1710.06592

Eigenvalue fluctuations for lattice Anderson Hamiltonians: Unbounded potentials

Marek Biskup·Ryoki Fukushima·Wolfgang Koenig
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Abstract

We consider random Schrödinger operators with Dirichlet boundary conditions outside lattice approximations of a smooth Euclidean domain and study the behavior of its lowest-lying eigenvalues in the limit when the lattice spacing tends to zero. Under a suitable moment assumption on the random potential and regularity of the spatial dependence of its mean, we prove that the eigenvalues of the random operator converge to those of a deterministic Schrödinger operator. Assuming also regularity of the variance, the fluctuation of the random eigenvalues around their mean are shown to obey a multivariate central limit theorem. This extends the authors' recent work where similar conclusions have been obtained for bounded random potentials.

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Marek Biskup, Ryoki Fukushima, Wolfgang Koenig. 2017-10-18. Eigenvalue fluctuations for lattice Anderson Hamiltonians: Unbounded potentials. https://doi.org/10.4036/iis.2018.a.03

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