01-296 Joseph G. Conlon

Homogenization of Random Walk in Asymmetric Random Environment (88K, LaTex 2e) Aug 3, 01

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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.

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