A new stochastic discrete space-time model of multiple random walkers
is proposed to simulate one- and two-dimensional many body interacting
lattice gas systems. A very simple rule set which prohibits the multi
ple occupancy of lattice sites by the random walkers while conserving
their number is used to define the dynamics of the walkers. We found a
linear time dependence for the mean squared end-to-end distances of t
he two-dimensional random walkers system. Extensions of the model to a
wide variety of diffusive systems are noted.