Probability of survival for vicious walkers near a cliff

Abstract

The partition function for a model system of N vicious walkers is expressed as a determinant when the walkers are confined to a half-line or a finite interval. For the walkers on the half-line, the probability of survival, the probability of a reunion and the conditional probability of a reunion are obtained. The two-point correlation near and parallel to a boundary of fixed like spins in the magnetised phase of the two-dimensional Ising model is conjectured to be proportional to the probability of a reunion near the boundary for N=2 and thus decay as e- xi zeta //r5 for large distances r.