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
Type
Article accepté pour publication ou publiéExternal document link
https://arxiv.org/abs/1404.4187v3Date
2015Journal name
Electronic Journal of ProbabilityVolume
20Publisher
Electronic Journal of Probability and Electronic Communications in Probability
Published in
Paris
Pages
42 p.
Publication identifier
Metadata
Show full item recordAbstract (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 / Keywords
Random walk in dynamic random environment; limit theorem; renormalization; renewal timesRelated items
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