The Ballistic Random Walker

We introduce and investigate the scaling properties of a random walker which moves ballistically on a square lattice, i.e., the walker is scattered (changes randomly direction) every time it reaches a previously non-visited site and follows ballistic trajectories meanwhile. This random walk is asymptotically sub-diffusive. The scaling exponent and the asymptotic properties of the density of non-visited sites can be calculated using a mean-field theory, and the obtained predictions are in good agreement with the results of extensive numerical simulations. (Dept767, Dept761)