Random walk driven by simple exclusion process
Résumé
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.
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
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