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

In this work, we study the spectral statistics for Anderson model on l(2)(N) with decaying randomness whose single-site distribution has unbounded support. Here, we consider the operator H-omega given by (H(omega)u)(n) = u(n+1) + u(n-1) + a(n)omega(n)u(n), a(n) similar to n(-alpha) and {omega(n)} are real i.i.d random variables following symmetric distribution mu with fat tail, i.e. mu((-R, R)(c)) < C/R-delta for R >> 1, for some constant C. In case of alpha - 1/delta > 1/2, we are able to show that the eigenvalue process in (-2, 2) is the clock process.