Abstract
We prove that random walks in i.i.d. random environments which oscillate in a given direction have velocity zero with respect to that direction. This complements existing results thus giving a general law of large numbers under the only assumption of a certain zero-one law, which is known to hold if the dimension is two.
Citation
Martin Zerner. "A Non-Ballistic Law of Large Numbers for Random Walks in I.I.D. Random Environment." Electron. Commun. Probab. 7 191 - 197, 2002. https://doi.org/10.1214/ECP.v7-1060
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