title: Optimal first-arrival times in Lévy flights with resetting.
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.
authors.affiliation: 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.
authors.forename: Łukasz
authors.initials: Ł
authors.lastname: Kuśmierz
authors.affiliation: 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.
authors.forename: Ewa
authors.initials: E
authors.lastname: Gudowska-Nowak