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The averages of ratios of characteristic polynomials det(lambda - X) of N x Nrandom matrices X, are investigated in the large N limit for the GUE, GOE andGSE ensemble. The density of states and the two-point correlation function arederived from these ratios. The method relies on an extension of theHarish-Chandra-Itzykson-Zuber integrals to the GOE ensemble and to supergroups,which are explicitly evaluated as solutions of heat kernel differentialequations. An external matrix source, linearly coupled to the random matrices,may also be added to the Gaussian distribution, and allows for a discussion ofuniversality of the GOE results in the large N limit.Comment: 61 pages, late

New correlation functions for random matrices and integrals over supergroups