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First-passage statistics under stochastic resetting in bounded domains
Umeå University, Faculty of Science and Technology, Department of Physics.
2019 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, no 22, article id 224001Article in journal (Refereed) Published
Abstract [en]

We investigate the first-passage problem where a diffusive searcher stochastically resets to a fixed position at a constant rate in a bounded domain. We put forward an analytical framework for this problem where the resetting rate r, the resetting position x r , the initial position x 0, the domain size L, and the particle's diffusion constant D are independent variables. From this we obtain analytical expressions for the mean-first passage time, survival probability and the first-passage time density in Laplace space in terms of the above independent variables, and closed forms in time-domain expression in some cases. For the first-passage time distributions their full-time profiles in time-domain are numerically obtained and validated by Monte Carlo simulations. We show that for the general resetting condition  the first-passage process has rich nontrivial features as it combines effects from resetting and the finiteness of the domain. A phase diagram showing the regions for resetting-enhanced and -suppressed first-passages is obtained analytically. Counter-intuitively, resetting facilitates the first-passage event even if the particle resets to a position that is further away from the target than where it started. Finally, we show that averaging over resetting positions, resetting never helps the search compared to a random search, unless the resetting position is displaced from the initial position.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2019. Vol. 52, no 22, article id 224001
Keywords [en]
first-passage time, stochastic resetting, bounded domain, optimal search
National Category
Other Physics Topics Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-159050DOI: 10.1088/1751-8121/ab15f5ISI: 000466752400001OAI: oai:DiVA.org:umu-159050DiVA, id: diva2:1317123
Available from: 2019-05-21 Created: 2019-05-21 Last updated: 2019-05-21Bibliographically approved

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Lizana, Ludvig

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CiteExportLink to record
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  • apa
  • ieee
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  • de-DE
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  • nn-NO
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Output format
  • html
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  • asciidoc
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