57 research outputs found
Spectral statistics for the discrete Anderson model in the localized regime
We report on recent results on the spectral statistics of the discrete
Anderson model in the localized phase. Our results show, in particular, that,
for the discrete Anderson Hamiltonian with smoothly distributed random
potential at sufficiently large coupling, the limit of the level spacing
distribution is that of i.i.d. random variables distributed according to the
density of states of the random Hamiltonian. This text is a contribution to the
proceedings of the conference "Spectra of Random Operators and Related Topics"
held at Kyoto University, 02-04/12/09 organized by N. Minami and N. Ueki
Lifshitz tails estimate for the density of states of the Anderson model
We prove an upper bound for the (differentiated) density of states of the
Anderson model at the bottom of the spectrum. The density of states is shown to
exhibit the same Lifshitz tails upper bound as the integrated density of
states
Enhanced Wegner and Minami estimates and eigenvalue statistics of random Anderson models at spectral edges
We consider the discrete Anderson model and prove enhanced Wegner and Minami
estimates where the interval length is replaced by the IDS computed on the
interval. We use these estimates to improve on the description of finite volume
eigenvalues and eigenfunctions obtained in a previous paper. As a consequence
of the improved description of eigenvalues and eigenfunctions, we revisit a
number of results on the spectral statistics in the localized regime and extend
their domain of validity, namely : - the local spectral statistics for the
unfolded eigenvalues; - the local asymptotic ergodicity of the unfolded
eigenvalues; In dimension 1, for the standard Anderson model, the improvement
enables us to obtain the local spectral statistics at band edge, that is in the
Lifshitz tail regime. In higher dimensions, this works for modified Anderson
models
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