Universal singularity at the closure of a gap in a random matrix theory

We consider a Hamiltonian H=H₀+V, in which H₀ is a given nonrandom Hermitian matrix, and V is an N×N Hermitian random matrix with a Gaussian probability distribution. We had shown before that Dyson's universality of the short-range correlations between energy levels holds at generic points of the spectrum independently of H₀. We consider here the case in which the spectrum of H₀ 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 H₀ is tuned so that the gap closes, a new class of universality appears for the energy correlations in the vicinity of this singular point.