Determinantal point processes associated with Bergman kernels

Abstract: Determinantal point processes (DPP) are point processes whose correlation functions are expressed as the determinant of an integral kernel on the ambient space. They often appear in models of particles with repulsive interactions, such as fermions, and have been studied extensively in quantum mechanics and random matrix theory. In this talk, I will describe a class of such processes on compact Kähler manifolds, first described by Berman a decade ago, whose correlation kernel is the Bergman kernel of a positive line bundle. In particular, I will show how the asymptotic expansion of the Bergman kernel, initiated by Tian, Catlin and Zelditch in the late 90's, translates into a universality phenomenon for these DPP.