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Article Dans Une Revue Electronic Journal of Probability Année : 2015

Random walk driven by the simple exclusion process

Résumé

We prove a 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 of the walker, 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 the fluctuations are normal.
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Dates et versions

hal-01099144 , version 1 (31-12-2014)
hal-01099144 , version 2 (08-01-2016)

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François Huveneers, François Simenhaus. Random walk driven by the simple exclusion process. Electronic Journal of Probability, 2015, 20 (105), pp.1-42. ⟨10.1214/EJP.v20-3906⟩. ⟨hal-01099144v2⟩
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