Mean arrival times of N regular and self avoiding random walkers

We investigate the mean first passage time for the first out of N identical . independently diffusing particles on polymers which are embedded in a d-d imensional Euclidean space. The polymers are modelled by self avoiding walk s. We obtain this arrival time in terms of a series in (lnN)(-1), independe nt of the dimension. We furthermore investigate the arrival time for partic les which diffuse in free space. but under the additional constraint that t hey are not allowed to cross their own trails, i.e. the particles themselve s perform self avoiding walks. In the latter case the N dependence of the m ean first passage time is modified to (lnN)(-(1-v)/v), where the Flory expo nent v describes how the mean end-to-end distance of a polymer increases wi th the number of monomers mt (r(m)) similar to m(v). We verify our predicti ons by numerical simulations of self avoiding walks and of random walks on self avoiding walks in d = 2.