We consider a Hamiltonian H = H-0 + V, in which H-0 is a given nonrandom Hermitian matrix, and V is an NXN Hermitian random matrix with a Gaussian probability distribution. We had shown before that Dyson's universality of the shea-range correlations between energy levels holds at generic points of the spectrum independently of H-0. We consider here the case in which the spectrum of H-0 is such that there is a gap in the average density of eigenvalues of H which is thus split into two pieces. When the spectrum of H-0 is tuned so that the gap closes, a new class of universality appears for the energy correlations in the vicinity of this singular point. [References: 22]
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