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Eigenvalue fluctuations for lattice Anderson Hamiltonians: Unbounded potentials. (arXiv:1710.06592v1 [math.PR])
来源于:arXiv
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. 查看全文>>