Order statistics of the trapping problem

Abstract

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 <t^m_{j,N}> 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 <t^m_{j,N}> for the one-dimensional lattice.

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

References in corpus (3)

• Diffusion with random distribution of static traps
• Order statistics for d-dimensional diffusion processes
• Multiparticle trapping problem in the half-line

Cited by in corpus (8)

• Some exact results for the trapping of subdiffusive particles in one dimension
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• Depletion of Resources by a Population of Diffusing Species
• On the joint residence time of N independent two-dimensional Brownian motions
• On the Mixing of Diffusing Particles
• Order statistics of Rosenstock's trapping problem in disordered media
• An encounter-based approach for restricted diffusion with a gradient drift