Optimal first-arrival times in Lévy flights with resetting

Łukasz Kuśmierz and Ewa Gudowska-Nowak
Phys. Rev. E 92, 052127 – Published 19 November 2015

Abstract

We consider the diffusive motion of a particle performing a random walk with Lévy distributed jump lengths and subject to a resetting mechanism, bringing the walker to an initial position at uniformly distributed times. In the limit of an infinite number of steps and for long times, the process converges to superdiffusive motion with replenishment. We derive a formula for the mean first arrival time (MFAT) to a predefined target position reached by a meandering particle and we analyze the efficiency of the proposed searching strategy by investigating criteria for an optimal (a shortest possible) MFAT.

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  • Received 12 August 2015

DOI:https://doi.org/10.1103/PhysRevE.92.052127

©2015 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Łukasz Kuśmierz

  • Marian Smoluchowski Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland and AGH University of Science and Technology, Department of Automatics and Biomedical Engineering, Al. Mickiewicza 30, 30-059, Kraków, Poland

Ewa Gudowska-Nowak

  • Marian Smoluchowski Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland and Mark Kac Complex Systems Research Center, Jagiellonian University, Kraków, Poland

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Issue

Vol. 92, Iss. 5 — November 2015

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