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This paper summarizes some work I've been doing on eigenvalue correlators ofRandom Matrix Models which show some interesting behaviour. First we considermatrix models with gaps in there spectrum or density of eigenvalues. Thedensity-density correlators of these models depend on whether N, where N is thesize of the matrix, takes even or odd values. The fact that this dependencepersists in the large N thermodynamic limit is an unusual property and may haveconsequences in the study of one electron effects in mesoscopic systems.Secondly, we study the parametric and cross correlators of the HarishChandra-Itzykson-Zuber matrix model. The analytic expressions determine how thecorrelators change as a parameter (e.g. the strength of a perturbation in thehamiltonian of the chaotic system or external magnetic field on a sample ofmaterial) is varied. The results are relevant for the conductance fluctuationsin disordered mesoscopic systems.Comment: 12 pages, Latex, 2 Figure

Parity effects in eigenvalue correlators, parametric and crossover correlators in random matrix models: Application to mesoscopic systems