2003/09/26 by S. B. Yuste, L. Acedo · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.68.036134
published as Phys. Rev. E 68, 036134 (2003) · 13 pages, RevTeX4, 8 eps figures
openalex publication_date 2003/09/26 · arxiv created 2003/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The distribution of times t(j,N) elapsed until the first j independent random walkers from a set of N>>1, all starting from the same site, are trapped by a quenched configuration of traps randomly placed on a disordered lattice is investigated. In doing so, the cumulants of the distribution of the territory explored by N independent random walkers S(N)(t), and the probability Phi(N)(t) that no particle of an initial set of N is trapped by time t are considered. Simulation results for the two-dimensional incipient percolation aggregate show that the ratio between the nth cumulant and the nth moment of S(N)(t) is, for large N, (i) very large in comparison with the same ratio in Euclidean media, and (ii) almost constant. The first property implies that, in contrast with Euclidean media, approximations of the order higher than the standard zeroth-order Rosenstock approximation are required to provide a reasonable description of the trapping order statistics. Fortunately, the second property (which has a geometric origin) can be exploited to build these higher-order Rosenstock approximations. Simulation results for the two-dimensional incipient percolation aggregate confirm the predictions of our approach.