We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas forâ€¦ (More)

We have found an exact formula expressing a general correlation function containing both products and ratios of characteristic polynomials of random Hermitian matrices. The answer is given in theâ€¦ (More)

Abstract We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three differentâ€¦ (More)

We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N Ã—N random matrix takenâ€¦ (More)

In the present paper we construct and solve a differential model for the q-analog of the Plancherel growth process. The construction is based on a deformation of the Makrov-Krein correspondenceâ€¦ (More)

In [41] H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polyno-mials. We obtain similar results forâ€¦ (More)

We calculate a general spectral correlation function of products and ratios of characteristic polynomials for a N Ã— N random matrix taken from the chiral Gaussian Unitary Ensemble (chGUE). Ourâ€¦ (More)

Normalized irreducible characters of the symmetric group S(n) can be understood as zonal spherical functions of the Gelfand pair (S(n)Ã—S(n),diag S(n)). They form an orthogonal basis in the space ofâ€¦ (More)

We distinguish a class of random point processes which we call Giambelli compatible point processes. Our definition was partly inspired by determinantal identities for averages of products and ratiosâ€¦ (More)

We present new and streamlined proofs of various formulae for products and ratios of characteristic polynomials of random Hermitian matrices that have appeared recently in the literature.