Diffusion with optimal resetting

Martin R. Evans, Satya N. Majumdar

Research output: Contribution to journalArticlepeer-review


We consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate r. We consider several generalizations of the model of Evans and Majumdar (2011 Phys. Rev. Lett. 106 160601): (i) a space-dependent resetting rate r(x); (ii) resetting to a random position z drawn from a resetting distribution P(z); and (iii) a spatial distribution for the absorbing target P-T (x). As an example of (i) we show that the introduction of a non-resetting window around the initial position can reduce the mean time to absorption provided that the initial position is sufficiently far from the target. We address the problem of optimal resetting, that is, minimizing the mean time to absorption for a given target distribution. For an exponentially decaying target distribution centred at the origin we show that a transition in the optimal resetting distribution occurs as the target distribution narrows.

Original languageEnglish
Article number435001
Number of pages15
JournalJournal of Physics A: Mathematical and Theoretical
Issue number43
Publication statusPublished - 11 Oct 2011


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