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Determinantal point processes associated with Bergman kernels

Wed
15
Feb
Time Wednesday 15 February, 2023 at 15:30 - 16:15
Place Zoom

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.

Event type: Seminar

Speaker: Thibaut Lemoine, Université de Lille

Contact
Antti Perälä
Read about Antti Perälä