ORDER STATISTICS FOR FIRST PASSAGE TIMES IN ONE-DIMENSIONAL DIFFUSION PROCESSES

摘要

The problem of the statistical description of the first passage time t(j,N) to one or two absorbing boundaries of the first j of a set of N independent diffusing particles in one dimension is revisited. An asymptotic expression for large N of the generating function of the moments of t(j,N) is obtained, and explicit expressions for the first two moments are presented. The results are valid for a specific but broad class of initial distributions of particles and boundaries. The mean first passage time of the first particle [t(1,N)] and its variance are compared with numerical estimates for an initial distribution in which all particles are placed al the midpoint of the diffusion region. [References: 8]