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Eigenvalue fluctuations for lattice Anderson Hamiltonians: Unbounded potentials
- Source :
- Interdisciplinary Information Sciences, 2018 Volume 24 Issue 1 Pages 59-76
- Publication Year :
- 2017
-
Abstract
- 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.<br />Comment: 25 pages
Details
- Database :
- arXiv
- Journal :
- Interdisciplinary Information Sciences, 2018 Volume 24 Issue 1 Pages 59-76
- Publication Type :
- Report
- Accession number :
- edsarx.1710.06592
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.4036/iis.2018.A.03