Continuous-time random walks under power-law resetting

Physical Review. E
Anna S Bodrova, Igor M Sokolov

Abstract

We study continuous-time random walks (CTRW) with power-law distribution of waiting times under resetting which brings the walker back to the origin, with a power-law distribution of times between the resetting events. Two situations are considered. Under complete resetting, the CTRW after the resetting event starts anew, with a new waiting time, independent of the prehistory. Under incomplete resetting, the resetting of the coordinate does not influence the waiting time until the next jump. We focus on the behavior of the mean-squared displacement (MSD) of the walker from its initial position, on the conditions under which the probability density functions of the walker's displacement show universal behavior, and on this universal behavior itself. We show, that the behavior of the MSD is the same as in the scaled Brownian motion (SBM), being the mean-field model of the CTRW. The intermediate asymptotics of the probability density functions (PDF) for CTRW under complete resetting (provided they exist) are also the same as in the corresponding case for SBM. For incomplete resetting, however, the behavior of the PDF for CTRW and SBM is vastly different.

References

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Mar 18, 2016·Physical Review. E·Vicenç Méndez, Daniel Campos
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Jan 20, 2018·Physical Review. E·V P Shkilev
Jun 20, 2019·Physical Review. E·Łukasz Kuśmierz, Ewa Gudowska-Nowak
Sep 11, 2019·Physical Review. E·Anna S BodrovaIgor M Sokolov
Sep 11, 2019·Physical Review. E·Anna S BodrovaIgor M Sokolov
Nov 28, 2019·Physical Review. E·Axel Masó-PuigdellosasVicenç Méndez
Jun 25, 2020·Physical Review. E·Anna S Bodrova, Igor M Sokolov

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Citations

Oct 21, 2020·Physical Review. E·Anna S Bodrova, Igor M Sokolov
Mar 20, 2021·Physical Review. E·Vicenç MéndezDaniel Campos

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