THE BROWNIAN VACANCY DRIVEN WALK

We investigate the lattice walk performed by a tagged member of an inf inite ''sea'' of particles filling a d-dimensional lattice, in the pre sence of a Brownian vacancy. Particle-particle exchange is forbidden; the only interaction between them being hard core exclusion. The tagge d particle, differing from the others only by its tag, moves only when it exchanges places with the hole. In this sense, it is a lattice wal k ''driven'' by the Brownian vacancy. The probability distributions fo r its displacement and for the number of steps taken, after n-steps of the vacancy, are derived. Surprisingly, none of them is a Gaussian! I t is shown that the only nontrivial dimensional where the walk is recu rrent is d=2.