New York Journal of Mathematics
Volume 11 (2005) 465-476


Joseph G. Conlon

Perturbation theory for random walk in asymmetric random environment

Published: October 29, 2005
Keywords: pde with random coefficients, homogenization
Subject: 35R60, 60H30, 60J60

In this paper the author continues his investigation into the scaling limit of a partial 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 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.

Author information

University of Michigan, Department of Mathematics, Ann Arbor, MI 48109-1109