Median and mode in first passage under restart
Restart—interrupting a stochastic process followed by a new start—is known to improve the mean time to its completion, and the general conditions under which such an improvement is achieved are now well understood. Here, we explore how restart affects other important metrics of first-passage phenome...
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| Format: | Article |
| Language: | English |
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American Physical Society
2020
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| Online Access: | https://hdl.handle.net/1721.1/126795 |
| _version_ | 1826208940357058560 |
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| author | Belan, Sergey |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Belan, Sergey |
| author_sort | Belan, Sergey |
| collection | MIT |
| description | Restart—interrupting a stochastic process followed by a new start—is known to improve the mean time to its completion, and the general conditions under which such an improvement is achieved are now well understood. Here, we explore how restart affects other important metrics of first-passage phenomena, namely, the median and the mode of the first-passage time distribution. Our analysis provides a general criterion for when restart lowers the median time and demonstrates that restarting is always helpful in reducing the mode. Additionally, we show that simple nonuniform restart strategies allow to optimize the mean and the median first-passage times, regardless of the characteristic timescales of the underlying process. These findings are illustrated with the canonical example of a diffusive search with resetting. |
| first_indexed | 2024-09-23T14:14:44Z |
| format | Article |
| id | mit-1721.1/126795 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:14:44Z |
| publishDate | 2020 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1267952022-09-28T19:29:17Z Median and mode in first passage under restart Belan, Sergey Massachusetts Institute of Technology. Department of Physics Restart—interrupting a stochastic process followed by a new start—is known to improve the mean time to its completion, and the general conditions under which such an improvement is achieved are now well understood. Here, we explore how restart affects other important metrics of first-passage phenomena, namely, the median and the mode of the first-passage time distribution. Our analysis provides a general criterion for when restart lowers the median time and demonstrates that restarting is always helpful in reducing the mode. Additionally, we show that simple nonuniform restart strategies allow to optimize the mean and the median first-passage times, regardless of the characteristic timescales of the underlying process. These findings are illustrated with the canonical example of a diffusive search with resetting. National Science Foundation (U.S.) (Grant DMR-1708280) 2020-08-25T14:49:16Z 2020-08-25T14:49:16Z 2020-03-03 2019-06 2020-03-03T15:16:38Z Article http://purl.org/eprint/type/JournalArticle 2643-1564 https://hdl.handle.net/1721.1/126795 Belan, Sergey. “Median and mode in first passage under restart.” Physical review research, 2, (March 2020): 013243 © 2020 The Author en http://dx.doi.org/10.1103/PhysRevResearch.2.013243 Physical review research Creative Commons Attribution 3.0 unported license http://creativecommons.org/licenses/by/3.0 application/pdf American Physical Society American Physical Society |
| spellingShingle | Belan, Sergey Median and mode in first passage under restart |
| title | Median and mode in first passage under restart |
| title_full | Median and mode in first passage under restart |
| title_fullStr | Median and mode in first passage under restart |
| title_full_unstemmed | Median and mode in first passage under restart |
| title_short | Median and mode in first passage under restart |
| title_sort | median and mode in first passage under restart |
| url | https://hdl.handle.net/1721.1/126795 |
| work_keys_str_mv | AT belansergey medianandmodeinfirstpassageunderrestart |