BALLISTIC RANDOM WALKER

We introduce and investigate the scaling properties of a random walker that moves ballistically on a two-dimensional square lattice. The wal ker is scattered (changes direction randomly) every time it reaches a previously unvisited site, and follows ballistic trajectories between two scattering events. The asymptotic properties of the density of unv isited sites and the diffusion exponent can be calculated using a mean -field theory. The obtained predictions are in good agreement with the results of extensive numerical simulations. In particular, we show th at this random walk is subdiffusive.