Random walk driven by simple exclusion process
Huveneers, François; Simenhaus, François (2015), Random walk driven by simple exclusion process, Electronic Journal of Probability, 20, p. 42 p.. 10.1214/EJP.v20-3906
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1404.4187v3
Journal nameElectronic Journal of Probability
Electronic Journal of Probability and Electronic Communications in Probability
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Abstract (EN)We prove strong law of large numbers and an annealed invariance principle for a random walk in a one-dimensional dynamic random environment evolving as the simple exclusion process with jump parameter γ. First we establish that, if the asymptotic velocity of the walker is non-zero in the limiting case "γ=∞" where the environment gets fully refreshed between each step, then, for γ large enough, the walker still has a non-zero asymptotic velocity in the same direction. Second we establish that if the walker is transient in the limiting case γ=0, then, for γ small enough but positive, the walker has a non-zero asymptotic velocity in the direction of the transience. These two limiting velocities can sometimes be of opposite sign. In all cases, we show that fluctuations are normal.
Subjects / KeywordsRandom walk in dynamic random environment; limit theorem; renormalization; renewal times
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