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Published: 
February 23, 2002

Keywords: 
random walk, homogenization, random environment

Subject: 
35R60, 60H30, 60J60

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
shows that the scaling limit, if it exists, depends on dimension. For
$d=1,2$ he provides evidence that the scaling limit cannot be diffusion.

Author information:
University of Michigan, Department of Mathematics, Ann Arbor, MI 481091109
conlon@math.lsa.umich.edu
http://www.math.lsa.umich.edu/~conlon/
 