Level Repulsion for a Class of Decaying Random Potentials

D. R. Dolai, M. Krishna

2015, v.21, №3, 449-462

ABSTRACT

In this paper we consider the Anderson model with decaying randomness and
show that statistics near the band edges in the absolutely continuous
spectrum in dimensions $d \geq 3$ is independent of the randomness and
agrees with that of the free part. We also consider the operators
at small coupling and identify the length scales at which the statistics
agrees with the free one in the limit when the coupling constant goes to zero.

Keywords: Anderson model, eigenvalue statistics, decaying potential

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