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Joseph G. Conlon

Homogenization of Random walk in Asymmetric Random Environment

Abstract: Consider a nearest neighbor random walk on the integer lattice in d dimensions. The transition probabilities are themselves random variables, independent from site to site and with no mean drift. It was shown by Sinai in 1982 that for d=1 the walk is with probability one strongly subdiffusive. In 1983-84 it was conjectured by Derrida and Luck and independently by Fisher, that for d>2 the walk is diffusive with probability one. In this lecture a series expansion is presented which may be a candidate for the effective diffusion constant in d>2. Showing that each term of the series is finite is non-trivial.