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Random walk driven by simple exclusion process

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Date
2015
Publisher city
Paris
Link to item file
https://arxiv.org/abs/1404.4187v3
Dewey
Probabilités et mathématiques appliquées
Sujet
Random walk in dynamic random environment; limit theorem; renormalization; renewal times
Journal issue
Electronic Journal of Probability
Volume
20
Publication date
2015
Article pages
42 p.
Publisher
Electronic Journal of Probability and Electronic Communications in Probability
DOI
http://dx.doi.org/10.1214/EJP.v20-3906
URI
https://basepub.dauphine.fr/handle/123456789/13153
Collections
  • CEREMADE : Publications
Metadata
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Author
Huveneers, François
Simenhaus, François
Type
Article accepté pour publication ou publié
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.

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