Eigenvalue Statistics for Lattice Hamiltonian with Off-diagonal Disorder

Abstract

This short note deals with a certain kind of lattice Hamiltonian with off-diagonal disorder. Based on the exponential decay of the fractional moment of the Green function, we are able to prove that the properly rescaled eigenvalues of the random Hamiltonian are distributed as a Poisson point process with intensity measure given by the density of states. One of the key step in this proof is the Minami-type estimate. As a crucial ingredient, we also use the Minami-type estimate to study some important properties of the random Hamiltonian, such as multiplicity of the eigenvalues and quantitative estimate of the localization centers.