Order statistics of the trapping problem.
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 mth 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 concentrations the mth 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.
Yuste
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SB
Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain.
Acedo
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