Renaud Raquépas: Limit theorems for recurrence-based estimators of entropy and entropy production

Abstract: Entropy and entropy production are mathematical quantities that are meant to capture “unpredictability” and “irreversibility” of processes, respectively. I will introduce these notions in the context of discrete processes, discuss sequences of recurrence-based quantities that can be used to estimate them, and finally present limit theorems that can be proved for these sequences. More precisely, I will present a law of large numbers obtained in collaboration with C. Cristadoro, M. Degli Esposti and V. Jaksic and a large deviation principle obtained in collaboration with N. Cuneo.