Eigenfunction Statistics for Anderson Model with Hölder continuous single site Potential

Abstract

We consider random Schrödinger operators on ${\ell }^2({\mathbb{Z}}^d)$ when the distribution of single site potentials is $\alpha$-Hölder continuous ($0<\alpha \le 1$). In localized regime we study the distribution of eigenfunctions simultaneously in space and energy. In a certain scaling limit we prove limits point are Poisson.

References in corpus (4)

• The Canopy Graph and Level Statistics for Random Operators on Trees
• Generalized eigenvalue-counting estimates for the Anderson model
• Eigenvalue statistics for random Schrodinger operators with non rank one perturbations
• Poisson Statistics for Anderson Model with Singular Randomness

Cited by in corpus (1)

• Global multiplicity bounds and Spectral Statistics Random Operators