On Weighted Random Band-Matrices with Dependences

Abstract

We develop techniques to compute the k-th Moment of the Eigenvalue-statistic for a random Matrix M the entries of which do not have to be necessarily Independent. The dependence is controlled via an equivalence relation on the pairs of the entries of M. Furthermore the entries are weighted, that means they are multiplied with a Riemann-integrable function on (0,1). Finally also weak convergence in probability of the Eigenvalue statsitic is discussed not for the weighted Matrix but also for band matrices the band-width of which behaves like o(N).