Affiliation: | (1) Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 55455, Minnesota;(2) Department of Mathematics, Princeton University, Princeton, New Jersey |
Abstract: | We give an exact computation of the second order term in the asymptotic expansion of the return probability, P2nd(0,0), of a simple random walk on the d-dimensional cubic lattice. We also give an explicit bound on the remainder. In particular, we show that P2nd(0,0) < 2 (d/4n)d/2 where n M=M(d) is explicitly given. |