Number of distinct sites visited byNparticles diffusing on a fractal

We study the mean number of distinct sites, ${\mathit{S}}_{\mathit{N}}$(t), visited up to time t by N≫1 noninteracting random walkers all starting from the same origin on a fractal substrate of dimension ${\mathit{d}}_{\mathit{f}}$. Using analytic arguments and numerical simulations, we find ${\mathit{S}}_{\mathit{N}}$(t)∼(lnN${)}_{\mathit{f}}^{\mathit{d}}$/δ${\mathit{t}}_{\mathit{s}}^{\mathit{d}}$/2 for fractals with spectral dimension ${\mathit{d}}_{\mathit{s}}$==2${\mathit{d}}_{\mathit{f}}$/${\mathit{d}}_{\mathit{w}}$<2, where δ==${\mathit{d}}_{\mathit{w}}$/(${\mathit{d}}_{\mathit{w}}$-1) and ${\mathit{d}}_{\mathit{w}}$ is the fractal dimension of a random walk.