In this paper the author continues his investigation into the scaling limit of a partial difference equation on the d-dimensional integer lattice Z^d, corresponding to a translation invariant random walk perturbed by a random vector field. In a previous paper he obtained a formula for the effective diffusion constant. It is shown here that for the nearest neighbor walk in dimension d≧ 3 this effective diffusion constant is finite to all orders of perturbation theory. The proof uses Tutte's decomposition theorem for 2-connected graphs into 3-blocks.

This research was partially supported by NSF under grant DMS-0138519.