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First passage and first hitting times of Lévy flights and Lévy walks

  • For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.

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Author:Vladimir V PalyulinORCiD, George Blackburn, Michael A LomholtORCiD, Nicholas W WatkinsORCiD, Ralf MetzlerORCiDGND, Rainer KlagesORCiDGND, Aleksei V. ChechkinORCiDGND
Parent Title (English):New Journal of Physics
Publisher:Dt. Physikalische Ges.
Place of publication:Bad Honnef
Document Type:Article
Date of first Publication:2019/10/11
Year of Completion:2019
Release Date:2019/12/04
Tag:Lévy flights; Lévy walks; first-hitting time; first-passage time
Funder:Universität Potsdam
Grant Number:PA 2019_97
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer Review:Referiert
Grantor:Publikationsfonds der Universität Potsdam
Publication Way:Open Access
Licence (English):License LogoCreative Commons - Attribution 3.0 Unported
Notes extern:Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 785