Date
2015
Publisher city
Paris
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
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.