Eigenvalue Fluctuations for Lattice Anderson Hamiltonians:Unbounded Potentials
Marek Tomasz Biskup, Ryoki Fukushima, Wolfgang König · Institutional Repositories DataBase (IRDB) · 2017
We consider random Schr"odinger 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 Schr"odinger 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. \end{abstract}