 

Joseph G. Conlon
Homogenization of Random Walk in Asymmetric Random Environment


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/

