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.
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Supported in part by grants from the Chevron Research Company and from Charles and Renée Taubman.
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Weiss, G.H., Shuler, K.E. & Lindenberg, K. Order statistics for first passage times in diffusion processes. J Stat Phys 31, 255–278 (1983). https://doi.org/10.1007/BF01011582
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DOI: https://doi.org/10.1007/BF01011582