Abstract
We consider random walks on Zd with transition ratesp(x, y) given by a random matrix. Ifp is a small random perturbation of the simple random walk, we show that the walk remains diffusive for almost all environmentsp ifd>2. The result also holds for a continuous time Markov process with a random drift. The corresponding path space measures converge weakly, in the scaling limit, to the Wiener process, for almost everyp.
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Communicated by T. Spencer
Dedicated to Joel Lebowitz on his 60th birthday
Supported by NSF-grant DMS-8903041
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Bricmont, J., Kupiainen, A. Random walks in asymmetric random environments. Commun.Math. Phys. 142, 345–420 (1991). https://doi.org/10.1007/BF02102067
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DOI: https://doi.org/10.1007/BF02102067