Order statistics for first passage times in diffusion processes |
| |
Authors: | George H Weiss Kurt E Shuler Katja Lindenberg |
| |
Institution: | 1. Division of Computer Research and Technology, National Institutes of Health, 20205, Bethesda, Maryland 2. Department of Chemistry, University of California, 92093, San Diego, La Jolla, California
|
| |
Abstract: | We consider the problem of the first passage times for absorption (trapping) of the firstj (j = 1,2, ....) ofk, j <k, identical and independent diffusing particles for the asymptotic case k?>1. Our results are a special case of the theory of order statistics. We show that in one dimension the mean time to absorption at a boundary for the first ofk diffusing particles, μ1,k , goes as (lnk)?1 for the set of initial conditions in which none of thek particles is located at a boundary and goes ask ?2 for the set of initial conditions in which some of thek particles may be located at the boundary. We demonstrate that in one dimension our asymptotic results (k21) are independent of the potential field in which the diffusion takes place for a wide class of potentials. We conjecture that our results are independent of dimension and produce some evidence supporting this conjecture. We conclude with a discussion of the possible import of these results on diffusion-controlled rate processes. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|