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Author: König, Wolfgang × End date: 2019 × Start date: 2019 × Start date: 2011 × Has files: Yes × Subject: homogenization ×

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    Eigenvalue fluctuations for lattice Anderson Hamiltonians: Unbounded potentials
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Biskup, Marek; Fukushima, Ryoki; König, Wolfgang
    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.