Probabilistic Cellular Automaton for Random Walkers

Abstract

A cellular automaton of multiple random walkers is proposed to simulate d-dimensional many-body interacting lattice gas system. The fully parallel dynamics of the random walkers in d-dimensional hyper cubic lattice system is defined by introducing a simple probabilistic local rule set which prohibits the multiple occupancy of the walkers on a lattice site and keeps the conservation of the total number at any time. An equation which essentially governs the dynamics is derived by constructing a Boltzmann transport equation. An expression for the diffusion constant is obtained analytically and compared with the simulation results.