William FitzGerald: Gap probabilities for random matrices and interacting particle systems

Abstract

The real eigenvalues of the real Ginibre ensemble, the real zeroes of a Gaussian power series and coalescing and annihilating particle systems are all examples of Pfaffian point processes. We prove Szegő-type asymptotic theorems for the corresponding Fredholm Pfaffian both in the ‘bulk’ and at the ‘edge’. This calculates the asymptotics of empty interval and non-crossing probabilities for a number of examples of Pfaffian point processes.