Order statistics of the trapping problem

Details Order statistics of the trapping problem Order statistics of the trapping problem

2001-10-09

arxiv.org/abs/cond-mat/0110172v1

Phys. Rev. E, vol. 64, 061107 (2001)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 7 figures, to be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.64.061107

When a large number N of independent diffusing particles are placed upon a site of a d-dimensional Euclidean lattice randomly occupied by a concentration c of traps, what is the m-th moment of the time t_{j,N} elapsed until the first j are trapped? An exact answer is given in terms of the probability Phi_M(t) that no particle of an initial set of M=N, N-1,..., N-j particles is trapped by time t. The Rosenstock approximation is used to evaluate Phi_M(t), and it is found that for a large range of trap concentracions the m-th moment of t_{j,N} goes as x^{-m} and its variance as x^{-2}, x being ln^{2/d} (1-c) ln N. A rigorous asymptotic expression (dominant and two corrective terms) is given for for the one-dimensional lattice.

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