Number of distinct sites visited by N particles diffusing on a fractal

We study the mean number of distinct sites, SN(t), visited up to time t by N1 noninteracting random walkers all starting from the same origin on a fractal substrate of dimension df. Using analytic arguments and numerical simulations, we find SN(t)∼(lnN)fd/δtsd/2 for fractals with spectral dimension ds==2df/dw<2, where δ==dw/(dw-1) and dw is the fractal dimension of a random walk.