XXII.—Random Paths in Two and Three Dimensions

Abstract

1. In a previous note (McCrea, 1936) the following problem was enunciated: A rectangular lattice is given; a particle P moves from one lattice-point to another in such a way that, when it is at any interior point, it is equally likely to move to any of its four neighbouring points. P is liberated at any given lattice-point and it is required to find the probability that it will ultimately reach any stated point in the boundary of the lattice, assuming that on arrival at a boundary point its movement ceases.