Apparaît dans la collection : 2017 - T2 - Stochastic Dynamics out of Equilibrium

We consider resetting a stochastic process by returning to the initial condition with a fixed rate. Resetting is a simple way of generating a nonequilibrium stationary state in the sense that the process is held away from any equilibrium state and a non-vanishing steady-state probability current is directed towards the resetting position. The nature and properties of nonequilibrium stationary state are questions of fundamental importance within statistical physics. Thus, the resetting paradigm provides a convenient framework within which to study such nonequilibrium properties. In these lecture we shall study some interesting properties of the resetting paradigm focussing mainly on the case of diffusion with stochastic resetting Lecture I: Diffusion with Stochastic resetting Motivation from search strategies; stationary state; survival probability with absorbing target; mean first passage time; renewal process and extreme value statistics interpretation. Lecture II: Many particle system Average and typical survival probabilities of a diffusing target; Relaxation dynamics and equilibration front. Lecture III General resetting-induced nonequilibrium stationary states; Generalised resetting and Optimisation Problems e. g. minimisation of mean time to locate a target; non Markovian resetting; open problems