Abstract

In this talk I will review the idea of stochastic resetting: by returning some dynamical process to its initial condition one can significantly change the behaviour of the process and indeed improve the typical time to complete some complex task. The essence of the idea is that by resetting one cuts off errant trajectories.I will discuss the simple example of a diffusive particle whose position is reset randomly in time with a constant rate r to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting:        (i) the system reaches a nontrivial nonequilibrium stationary state        (ii) the mean time for the particle to reach a target is rendered finite and has a minimum, optimal, value as a function of the resetting rate r.I will discuss recent developments including considering an additive resetting cost.