Striking universalities in stochastic resetting processes

Given a random process which undergoes stochastic resetting at a constant rate r to a position drawn from a distribution , we consider a sequence of dynamical observables associated to the intervals between resetting events. We calculate exactly the probabilities of various events related to this sequence: that the last element is larger than all previous ones, that the sequence is monotonically increasing, etc. Remarkably, we find that these probabilities are “super-universal”, i.e., that they are independent of the particular process , the observables A _k 's in question and also the resetting distribution . For some of the events in question, the universality is valid provided certain mild assumptions on the process and observables hold (e.g., mirror symmetry).