Splitting of a gap in the bulk of the spectrum of random matrices (Igor Krasovsky, Imperial College London, UK)

12.12.2016 15:15 – 17:15

We start with a short introduction to unitary invariant ensembles of random matrices using the example of the Gaussian Unitary Ensemble. We will describe the basic properties of the eigenvalues, in particular, their local behavior in the bulk of the spectrum and at the edges. The eigenvalues in the bulk of the spectrum of typical random matrices follow the sine kernel determinantal process. The asymptotics of the probability of a large gap, i.e. an interval without eigenvalues, and that for a logarithmic derivative of the probability for several large gaps is well known. In this talk we will present the description of the transition regime between the asymptotic behavior of the probability for one gap and that for two gaps. This regime corresponds to the beginning of the splitting of one gap into two. The talk is based on a joint work with Benjamin Fahs.

Lieu

Room 623 15:15-16:00 & Room 17 16:30-17:15, Séminaire "Mathématique Physique"

entrée libre