Nonuniversality of compact support probability distributions in random matrix theory

The two-point resolvent is calculated in the large-$n$ limit for the generalized fixed and bounded trace ensembles. It is shown to disagree with that of the canonical Gaussian ensemble by a nonuniversal part that is given explicitly for all monomial potentials ${V\left(M\right)=M}^{2p}.$ Moreover, we prove that for the generalized fixed and bounded trace ensemble all k-point resolvents agree in the large-$n$ limit, despite their nonuniversality.