Can I read Distribution of Extreme First Passage Times of Diffusion on EtoBox?

Distribution of Extreme First Passage Times of Diffusion by Sean D. Lawley is a Biochemistry, Genetics and Molecular Biology article available to read on EtoBox.

What is Distribution of Extreme First Passage Times of Diffusion about?

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.

Who reads Distribution of Extreme First Passage Times of Diffusion?

Author

Sean D. Lawley

Publisher

Springer; Springer-Verlag; Springer Verlag; Springer Science and Business Media LLC; Society for Mining, Metallurgy and Exploration Inc. (ISSN 0303-6812)

Published

2020

Language

EN

Field

Biochemistry, Genetics and Molecular Biology (Life Sciences)