Fastest first-passage time statistics for time-dependent particle injection
A common scenario in a variety of biological systems is that multiple particles are searching in parallel for an immobile target located in a bounded domain, and the fastest among them that arrives to the target first triggers a given desirable or detrimental process. The statistics of such extreme...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2025-06-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.023239 |
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| Summary: | A common scenario in a variety of biological systems is that multiple particles are searching in parallel for an immobile target located in a bounded domain, and the fastest among them that arrives to the target first triggers a given desirable or detrimental process. The statistics of such extreme events—the fastest first-passage to the target—is well-understood by now through a series of theoretical analyses, but exclusively under the assumption that all N particles start simultaneously, i.e., all are introduced into the domain instantly, by δ-function-like pulses. However, in many practically important situations this is not the case: to start their search, the particles often have to enter first into a bounded domain, e.g., a cell or its nucleus, penetrating through gated channels or nuclear pores. This entrance process has a random duration so that the particles appear in the domain sequentially and with a time delay. Here we focus on the effect of such an extended-in-time injection of multiple particles on the fastest first-passage time (fFPT) and its statistics. We derive the full probability density function H_{N}(t) of the fFPT with an arbitrary time-dependent injection intensity of N particles. Under rather general assumptions on the survival probability of a single particle and on the injection intensity, we derive the large-N asymptotic formula for the mean fFPT, which is quite different from that obtained for the instantaneous δ-pulse injection. The extended injection is also shown to considerably slow down the convergence of H_{N}(t) to its large-N limit—the Gumbel distribution—so that the latter may be inapplicable in the most relevant settings with few tens to few thousands of particles. |
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| ISSN: | 2643-1564 |