Sorting single events: mean arrival times of N random walkers

Using a scaling approach we investigate the first passage time < mu(1,N)(r)> for the first out of N identical independently diffusing particles in ordered and disordered structures. For Euclidean spaces we obtain < mu(1,N)(r)> in terms of a series in (ln N)(-1), independent of dimension. In the case of disordered ramified fractals < mu(1,N)(r)> is expressed in terms of a series in (ln N)((1-d(l)(w))), where d(l)(w) describes how the mean topological distance evolves with time t. We propose a scaling behavior for the related quantity S(N)(t), the number of distinct sites visited by N particles. We verify our predictions by numerical simulations.