Clock statistics for 1d Schrodinger operators

We study the 1d Schrodinger operators with alloy type random supercritical decaying potential, where the random variables {omega(j)}(j is an element of Z) in the potential are either i.i.d. or more generally ones with exponentially decaying correlations. We prove the convergence to the clock process for the local statistics of eigenvalues. Moreover we prove the strong clock behavior in i.i.d. case.