An exact closed form solution for the return probability of a random walk on
the Bethe lattice is given. The long-time asymptotic form confirms a previously
known expression. It is however shown that this exact result reduces to the
proper expression when the Bethe lattice degenerates on a line, unlike the
asymptotic result which is singular. This is shown to be an artefact of the
asymptotic expansion. The density of states is also calculated.Comment: 7 pages, RevTex 3.0, 2 figures available upon request from
[email protected], to be published in J.Phys.A Let