Look Who it Was Random video

Stochastic Resetting - Lecture 1

1,211 views · Published 9 May 2017 · 1:29:17 · Indexed 20 September 2026

Channel: Institut Henri Poincaré · 2017 · Science & Technology

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By Martin Evans (Edinburgh)
Abstract: 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

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