Antoine Doeraene (UCLouvain) : On the Airy Ensemble and its generating function

Wednesday 25 Jan 2017, 15:00 → 17:00 Europe/Brussels

CYCL09 (MdeHemptinne)

Abstract: The Airy Ensemble is a determinantal point process that appears as a limiting process in a wide range of mathematical and physical models. For instance, it is obtained when scaling at the edge of the spectrum of the well known GUE ensemble, hence describing the near extreme eigenvalue statistics. The generating function of the few largest particles of the Airy Ensemble may be expressed in terms of a Fredholm Determinant. For some simple cases, this determinant has been related to a certain solution of the Painlevé II equation and the celebrated Tracy-Widom distribution. We want to give a more general description of this Fredholm determinant.