We introduce and investigate the scaling properties of a random walker that moves ballistically on a two-dimensional square lattice. The walker 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 unvisited 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 that this random walk is subdiffusive. © 1996 The American Physical Society.

• Received 7 February 1996

DOI:https://doi.org/10.1103/PhysRevE.54.968