Continuous time random walks under Markovian resetting

Vicenc Mendez*, Axel Maso-Puigdellosas, Trifce Sandev, Daniel Campos

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

23 Citations (Scopus)

Abstract

We investigate the effects of Markovian resetting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power-law probability density functions. We prove the existence of a nonequilibrium stationary state and finite mean first arrival time. However, the existence of an optimum reset rate is conditioned to a specific relationship between the exponents of both power-law tails. We also investigate the search efficiency by finding the optimal random walk which minimizes the mean first arrival time in terms of the reset rate, the distance of the initial position to the target, and the characteristic transport exponents.

Original languageEnglish
Article number022103
Number of pages8
JournalPhysical Review E
Volume103
Issue number2
DOIs
Publication statusPublished - 3 Feb 2021

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