Current fluctuations of a system of one-dimensional random walks in random environment

Abstract

We study the current of particles that move independently in a common static random environment on the one-dimensional integer lattice. A two-level fluctuation picture appears. On the central limit scale the quenched mean of the current process converges to a Brownian motion. On a smaller scale the current process centered at its quenched mean converges to a mixture of Gaussian processes. These Gaussian processes are similar to those arising from classical random walks, but the environment makes itself felt through an additional Brownian random shift in the spatial argument of the limiting current process.

Published in at http://dx.doi.org/10.1214/10-AOP537 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (7)

• $t^{1/3}$ Superdiffusivity of Finite-Range Asymmetric Exclusion Processes on $\mathbb{Z}$
• On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion
• Quenched limits for transient, zero speed one-dimensional random walk in random environment
• Limiting distributions and large deviations for random walks in random environments
• Second-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks
• Space-Time Current Process for Independent Random Walks in One Dimension
• Current and density fluctuations for interacting particle systems with anomalous diffusive behavior