Joseph G. Conlon
Homogenization of Random Walk
in Asymmetric Random Environment
(88K, LaTex 2e)
ABSTRACT. In this paper, the author investigates 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 the
case when the translation invariant walk scales to a Cauchy process he
proves convergence to an effective equation on $\R^d$. The effective equation
corresponds to a Cauchy process perturbed by a constant vector field. In the
case when the translation invariant walk scales to Brownian motion he
proves that the scaling limit, if it exists, depends on dimension. For
$d=1,2$ the scaling limit cannot be diffusion.