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 orde red 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 o f disordered ramified fractals [mu(1,N)(r)] is expressed in terms of a seri es in (ln N)((1-dw)), where d(w)(l) describes how the mean topological dist ance [l(t)] evolves with time t. We propose a scaling behavior for the rela ted quantity S-N(t), the number of distinct sites visited by N particles. W e verify our predictions by numerical simulations. [S1063-651X(99)10612-3].