Title: On the asymptotic behaviour of the pure complex spectrum probability for the real Ginibre ensemble
Abstract: We discuss a new result for the probability that a large real Ginibre matrix has no or very few real eigenvalues. The asymptotic behaviour of the probability can be guessed by using a deep connection between the real eigenvalues process and Annihilating Brownian Motions (ABM's), first discovered in papers of R. Tribe and O. Zaboronski. We give a rigorous proof of the guess by using the determinant representation of the probability. We also show how to exploit the connection between ABM's to and the real Ginibre ensemble to predict the asymptotic behaviour of the biggest real eigenvalue. The talk is based on a joint paper with E.Kanzieper, C.Timm, R.Tribe, O.Zaboronski.