Level Crossing in Random Matrices: I. Random perturbation of a fixed matrix

Research paper by B. Shapiro, K. Zarembo

Indexed on: 10 Mar '16Published on: 10 Mar '16Published in: Mathematical Physics

Abstract

We consider level crossing in a matrix family $H=H_0+\lambda V$ where $H_0$ is a fixed $N\times N$ 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 $\lambda$, for which we obtain a number of exact, asymptotic and approximate formulas.