ArticleJournal of mathematical biology2020
Distribution of extreme first passage times of diffusion.
Article in Journal of mathematical biology, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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Who cites it
7 citing papers in PubMed.
- Kinetic Monte Carlo methods for three-dimensional diffusive capture problems in exterior domains.Royal Society open science · 2025Article
- Fast decisions reflect biases; slow decisions do not.Physical review. E · 2024Article
- Diffusive coupling facilitates and impedes noise-induced escape in interacting bistable elements.Scientific reports · 2024Article
- Article
- Single-cell directional sensing from just a few receptor binding events.Biophysical journal · 2023Article
- Modulation of antigen discrimination by duration of immune contacts in a kinetic proofreading model of T cell activation with extreme statistics.PLoS computational biology · 2023Article
- Short-time diffusive fluxes over membrane receptors yields the direction of a signalling source.Royal Society open science · 2023Article
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1 author.
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Abstract
Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However, the more relevant timescale in many biological systems is the time it takes the fastest searcher(s) out of many searchers to find a target, which is called an extreme FPT. In this paper, we apply extreme value theory to find a tractable approximation for the full probability distribution of extreme FPTs of diffusion. This approximation can be easily applied in many diverse scenarios, as it depends on only a few properties of the short time behavior of the survival probability of a single FPT. We find this distribution by proving that a careful rescaling of extreme FPTs converges in distribution as the number of searchers grows. This limiting distribution is a type of Gumbel distribution and involves the LambertW function. This analysis yields new explicit formulas for approximations of statistics of extreme FPTs (mean, variance, moments, etc.) which are highly accurate and are accompanied by rigorous error estimates.
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