Dynamics of unvisited sites in the presence of mutually repulsive random walkers

We have considered the persistence of unvisited sites of a lattice, i.e., the probability S(t) that a site remains unvisited till time t in the presence of mutually repulsive random walkers in one dimension. The dynamics of this system has direct correspondence to that of the domain walls in a certain system of Ising spins where the number of domain walls becomes fixed following a zero-temperature quench. Here we get the result that S(t) proportional to exp(-alpha t(beta)) where beta is close to 0.5 and a a function of the density of the walkers rho. The fraction of persistent sites in the presence of independent walkers of density rho' is known to be S'(t) = exp (-2v root 2/pi rho't(1/2)). We show that a mapping of the interacting walkers' problem to the independent walkers' problem is possible with. rho =rho/(1-rho) provided rho' and rho are small. We also discuss some other intricate results obtained in the interacting walkers' case.