Perturbation theory for random walk in asymmetric random environment (Q2583040)

The author continues his investigation w.r.t. the scaling limit of a partial difference equation on the \(d\)-dimensional integer lattice \({\mathbb Z}^d\), 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 \(d\geq 3\) this effective diffusion constant is finite to all orders of perturbation theory. At the level of formal perturbation theory it means that random walk in asymmetric environment is diffusive at large time. The proof uses Tutte's decomposition theorem for 2-connected graphs into 3-blocks.