Spectral statistics for one-dimensional Anderson model with unbounded but decaying potential

Abstract

In this work, we study the spectral statistics for Anderson model on [Formula: see text] with decaying randomness whose single-site distribution has unbounded support. Here, we consider the operator [Formula: see text] given by [Formula: see text], [Formula: see text] and [Formula: see text] are real i.i.d random variables following symmetric distribution [Formula: see text] with fat tail, i.e. [Formula: see text] for [Formula: see text], for some constant [Formula: see text]. In case of [Formula: see text], we are able to show that the eigenvalue process in [Formula: see text] is the clock process.