WIAS Preprint No. 2439, (2017)

Eigenvalue fluctuations for lattice Anderson Hamiltonians: Unbounded potentials



Authors

  • Biskup, Marek
  • Fukushima, Ryoki
  • König, Wolfgang

2010 Mathematics Subject Classification

  • 60H25 82B44 35P20 74Q15 47A75 47H40

Keywords

  • Random Schrödinger operator, Anderson Hamiltonian, eigenvalue, spectral statistics, homogenization, central limit theorem

DOI

10.20347/WIAS.PREPRINT.2439

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. endabstract

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