Journal of Statistical Physics, Vol. 52, Nos l/2, 1988. p. 287-293.
We derive the probability density for a simple measure of the asymmetry of a one-dimensional random walk, namely the ratio of the minimum of the two maximum displacements in the positive and negative directions, to the maximum. We show that in the diffusion limit the asymmetry is independent of time. These results are shown to apply to random walks in which individual steps have a stable law distribution as well as to multidimensional random walks.