Large Deviations in Self-Interacting Processes

I will present recent results on large-deviation asymptotics for self-interacting processes - non-Markovian systems whose dynamics depend on their own empirical occupation measures. In particular, I will discuss a level-2.5 large deviation principle for self-interacting jump processes, whose rate function can be interpreted as a dynamical extension of the classical Donsker–Varadhan rate function for Markov processes. I will sketch the main ideas behind the proof and illustrate the framework through examples and applications, including, time permitting, kinetic and thermodynamic bounds.