Level crossing in random matrices: I. Random perturbation of a fixed matrix. (23rd December 2016) - Shapiro, B; Zarembo, K
Abstract: We consider level crossing in a matrix family H = H 0 + λ V where H 0 is a fixed N × N matrix and V belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing points in the complex plane of λ, for which we obtain a number of exact, asymptotic and approximate formulas.