Multiparticle trapping problem in the half-line

A variation of Rosenstock's trapping model in which N independent random wa lkers are all initially placed upon a site of a one-dimensional. lattice in the presence of a one-sided random distribution (with probability c) of ab sorbing traps is investigated. The probability (survival probability) Phi ( N)(t) that no random walker is trapped by time t for N much greater than 1 is calculated by using the extended Rosenstock approximation. This requires the evaluation of the moments of the number SN(t) of distinct sites visite d in a given direction up to time t by N independent random walkers. The Ro senstock approximation improves when N increases, working well in the range Dtln(2)(1 - c) much less than ln N, D being the diffusion constant. The mo ments of the time (lifetime) before any trapping event occurs are calculate d asymptotically, too. The agreement with numerical results is excellent. ( C) 2001 Elsevier Science B.V. All rights reserved.