Wigner's matrices; more moments estimates

Abstract

In this chapter, we elaborate upon the previous computation of moments in two directions. First we give a better estimate of the error to the previous limit and prove a central limit theorem. Second, we consider the case where moments are taken at powers that blow up with the dimension of the matrices; we basically show that if this power is small compared to the square root of the dimension, the first-order contribution is still given, in the moment expansion, by graphs that are trees.