Coupled Random Walks: Vicious Walkers, and a Lamb Besieged by a Pride of Lions

Consider N+1 random walkers on the line. The relative ordering of the walkers' positions poses interesting questions in probability theory. For example, the survival probability of the original ordering (no crossings allowed) up to time t is known as the problem of "vicious walkers". The probability that the leftmost walker remains to the left of all others is known as that of "the lamb and lions": we may think of the walker as a lamb that is devoured upon encounter with any of the N remaining walkers -- the lions. In this talk I will review the ordering problem, known results and approaches, and I will present an exact mapping to an electrostatic problem. The latter involves the Laplace equation with a point source in a semi-infinite N-dimensional wedge, with Dirichlet boundary conditions. New results for N > 2 will be derived from this mapping.