Random walk with resetting in a 1D chain

1Christophorov, LN
1Bogolyubov Institute for Theoretical Physics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2020, 8:43-50
Section: Physics
Language: Ukrainian

If the classical model of random walks is added with the stochastic resetting to the starting point, then the whole process acquires new nontrivial features. In particular, there appears a non-equilibrium steady state. In addition, the mean first passage time (which is infinite in the absence of restarts) becomes finite and can be optimized by choosing a proper mean intermittence frequency r. It is shown that, in the case of random walks on the nodes of a one-dimensional chain, these effects essentially differ from their analogs within the classical continuous diffusion model. In particular, the asymptotes of the dependences of stationary node populations on r change from exponential to power ones. Similar qualitative and quantitative distinctions take place for the mean first passage time as well. In the case of a finite chain, the interesting effect of emergence and disappearance of a possibility of the minimization of this time, depending on the distance to a defined target, shows up.

Keywords: first passage time, low-dimensional lattices, random walk, stochastic resetting

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