Giulio Ruzza - Determinantal Point Processes and Integrable PDEs

Abstract: I will explain how multiplicative statistics of universal determinantal point processes are connected to integrable PDEs. For instance, all cylindrical KdV solutions can be constructed from the Airy determinantal point process as multiplicative expectations, or, more generally, as Jánossy densities. The methods of integrable systems, particularly Riemann-Hilbert techniques, can be applied to asymptotic problems in probability theory. Specifically, I will outline an application to the tail asymptotics of cylindrical KdV and of narrow-wedge KPZ solutions. This talk is based on joint works with Mattia Cafasso, Christophe Charlier, Tom Claeys, Gabriel Glesner, and Sofia Tarricone.