Correlation Estimates in the Anderson Model |
| |
Authors: | Jean V Bellissard Peter D Hislop Günter Stolz |
| |
Institution: | (1) Georgia Institute of Technology, School of Mathematics, Atlanta, GA 30332-0160, USA;(2) Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA;(3) Department of Mathematics, UAB, Birmingham, AL 35294-1170, USA |
| |
Abstract: | 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. |
| |
Keywords: | Eigenvalue statistics Random operators Wegner estimate |
本文献已被 SpringerLink 等数据库收录! |
|