Poisson statistics of eigenvalues in the hierarchical Anderson model
arXiv:0710.2582 · doi:10.1007/s00023-008-0369-5
Abstract
We study the eigenvalue statistics for the hieracharchial Anderson model of Molchanov. We prove Poisson fluctuations at arbitrary disorder, when the the model has spectral dimension d<1. The proof is based on Minami's technique and we give an elementary exposition of the probabilistic arguments.