Abstract

Self-interacting diffusions provide a tractable framework to study stochastic dynamics with non-Markov feedback. I will begin by presenting results on current fluctuations in such systems on a ring, where non-Markovian interactions lead to a phase transition from self-repelling to self-attracting behaviour. Using an upper bound of level 2.5 large deviations, I estimate rare current fluctuations and identify the onset of localisation. I will then turn to escape dynamics in a feedback-modified Ornstein–Uhlenbeck process. Here, time-averaged feedback reshapes the most probable escape paths by lowering the effective energy barrier. Together, these results illustrate how memory and feedback fundamentally alter rare event statistics in stochastic systems, potentially offering new handles for control.