Perturbation theory for random walk in asymmetric random environment

摘要

In this paper the author continues his investigation into the scaling limit of apartial difference equation on the d-dimensional integer lattice Zd, corresponding to a translation invariant random walk perturbed by a random vector field. In a previous paper he obtained a formula for the effectivediffusion constant. It is shown here that for the nearest neighbor walk indimension d≧ 3 this effective diffusion constant is finite to all orders ofperturbation theory. The proof uses Tutte's decomposition theorem for2-connected graphs into 3-blocks.