2007/03/20 by Jean Bellissard, Jean V. Bellissard, Peter D. Hislop +1 · 1 citation
Mathematics · Physics and Astronomy · #Numerical methods in inverse problems #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:81Q19 #msc:82B44
paper · pdf · doi:10.1007/s10955-007-9409-7
16 pages
arxiv created 2007/03/20 · openalex publication_date 2007/09/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
We give a new proof of correlation estimates for arbitrary moments of the resolvent of random Schrödinger operators on the lattice that generalizes and extends the correlation estimate of Minami for the second moment. We apply this moment bound to obtain a new n-level Wegner-type estimate that measures eigenvalue correlations through an upper bound on the probability that a local Hamiltonian has at least n eigenvalues in a given energy interval. Another consequence of the correlation estimates is that the results on the Poisson statistics of energy level spacing and the simplicity of the eigenvalues in the strong localization regime hold for a wide class of translation-invariant, selfadjoint, lattice operators with decaying off-diagonal terms and random potentials.