Title | Random walk with resetting in a 1D chain |
Publication Type | Journal Article |
Year of Publication | 2020 |
Authors | Christophorov, LN |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2020.08.043 |
Issue | 8 |
Section | Physics |
Pagination | 43-50 |
Date Published | 8/2020 |
Language | Ukrainian |
Abstract | 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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