English

Diffusion with Optimal Resetting

Statistical Mechanics 2015-11-24 v2 Mathematical Physics math.MP

Abstract

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 rr. We consider several generalisations of the model of M. R. Evans and S. N. Majumdar (2011), Diffusion with stochastic resetting, Phys. Rev. Lett. 106, 160601: (i) a space dependent resetting rate r(x)r(x) ii) resetting to a random position zz drawn from a resetting distribution P(z){\cal P}(z) iii) a spatial distribution for the absorbing target PT(x)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, minimising 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.

Keywords

Cite

@article{arxiv.1107.4225,
  title  = {Diffusion with Optimal Resetting},
  author = {Martin R. Evans and Satya N. Majumdar},
  journal= {arXiv preprint arXiv:1107.4225},
  year   = {2015}
}

Comments

17 pages, 2 figures, submitted to J. Phys. A: Math. Theor, abstract corrected

R2 v1 2026-06-21T18:39:57.600Z