Benjamin Fahs (Imperial)

On the probability of finding two large gaps in the spectrum of random matrices

The sine process is the simplest and one of the most well-studied determinantal processes appearing in random matrix theory. For example, it occurs as the bulk scaling limit of the Gaussian Unitary Ensemble. We will discuss gap probabilities for the sine process, and present recent joint work with I. Krasovsky on the asymptotic probability of observing two large gaps.