Asymptotics of extreme statistics of escape time in 1,2 and 3-dimensional diffusions
Subcellular Processes
2018-10-17 v1 Probability
Data Analysis, Statistics and Probability
Abstract
The first of identical independently distributed (i.i.d.) Brownian trajectories that arrives to a small target, sets the time scale of activation, which in general is much faster than the arrival to the target of only a single trajectory. Analytical asymptotic expressions for the minimal time is notoriously difficult to compute in general geometries. We derive here asymptotic laws for the probability density function of the first and second arrival times of a large number of i.i.d. Brownian trajectories to a small target in 1,2, and 3 dimensions and study their range of validity by stochastic simulations. The results are applied to activation of biochemical pathways in cellular transduction.
Keywords
Cite
@article{arxiv.1711.01330,
title = {Asymptotics of extreme statistics of escape time in 1,2 and 3-dimensional diffusions},
author = {Kanishka Basnayake and Claire Guerrier and Zeev Schuss and David Holcman},
journal= {arXiv preprint arXiv:1711.01330},
year = {2018}
}
Comments
6 figs