EXACT SOLUTION OF THE LOCK STEP MODEL OF VICIOUS WALKERS

The lock step model of vicious walkers on a one-dimensional lattice allows each walker at the tick of a clock to move either one lattice site to the left or one lattice site to the right. The only restriction is that no two walkers may arrive at the same lattice site or pass one another. In periodic boundary conditions the partition function and correlation function for this model are calculated exactly. Taking the continuum limit gives an exactly solvable model of vicious walkers undergoing Brownian motion.