First-passage properties of asymmetric Levy flights
- Lévy flights are paradigmatic generalised random walk processes, in which the independent stationary increments—the 'jump lengths'—are drawn from an -stable jump length distribution with long-tailed, power-law asymptote. As a result, the variance of Lévy flights diverges and the trajectory is characterised by occasional extremely long jumps. Such long jumps significantly decrease the probability to revisit previous points of visitation, rendering Lévy flights efficient search processes in one and two dimensions. To further quantify their precise property as random search strategies we here study the first-passage time properties of Lévy flights in one-dimensional semi-infinite and bounded domains for symmetric and asymmetric jump length distributions. To obtain the full probability density function of first-passage times for these cases we employ two complementary methods. One approach is based on the space-fractional diffusion equation for the probability density function, from which the survival probability is obtained for differentLévy flights are paradigmatic generalised random walk processes, in which the independent stationary increments—the 'jump lengths'—are drawn from an -stable jump length distribution with long-tailed, power-law asymptote. As a result, the variance of Lévy flights diverges and the trajectory is characterised by occasional extremely long jumps. Such long jumps significantly decrease the probability to revisit previous points of visitation, rendering Lévy flights efficient search processes in one and two dimensions. To further quantify their precise property as random search strategies we here study the first-passage time properties of Lévy flights in one-dimensional semi-infinite and bounded domains for symmetric and asymmetric jump length distributions. To obtain the full probability density function of first-passage times for these cases we employ two complementary methods. One approach is based on the space-fractional diffusion equation for the probability density function, from which the survival probability is obtained for different values of the stable index and the skewness (asymmetry) parameter . The other approach is based on the stochastic Langevin equation with -stable driving noise. Both methods have their advantages and disadvantages for explicit calculations and numerical evaluation, and the complementary approach involving both methods will be profitable for concrete applications. We also make use of the Skorokhod theorem for processes with independent increments and demonstrate that the numerical results are in good agreement with the analytical expressions for the probability density function of the first-passage times.…
Verfasserangaben: | Amin PadashORCiD, Aleksei V. ChechkinORCiDGND, Bartlomiej DybiecORCiD, Ilya PavlyukevichORCiDGND, Babak ShokriORCiD, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1088/1751-8121/ab493e |
ISSN: | 1751-8113 |
ISSN: | 1751-8121 |
Titel des übergeordneten Werks (Englisch): | Journal of physics : A, Mathematical and theoretical |
Verlag: | IOP Publ. Ltd. |
Verlagsort: | Bristol |
Publikationstyp: | Wissenschaftlicher Artikel |
Sprache: | Englisch |
Jahr der Erstveröffentlichung: | 2019 |
Erscheinungsjahr: | 2019 |
Datum der Freischaltung: | 06.10.2020 |
Freies Schlagwort / Tag: | Levy flights; first-passage; search dynamics |
Band: | 52 |
Ausgabe: | 45 |
Seitenanzahl: | 48 |
Fördernde Institution: | Ministry of Science, Research and Technology of Iran; University of Potsdam; PLGrid Infrastructure; DFGGerman Research Foundation (DFG) [ME 1535/7-1]; Foundation for Polish Science within an Alexander von Humboldt Polish Honorary Research Scholarship |
Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC-Klassifikation: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer Review: | Referiert |
Publikationsweg: | Open Access |
Open Access / Hybrid Open-Access |