The Annals of Probability

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

Jonathon Peterson and Timo Seppäläinen

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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.

Article information

Source
Ann. Probab., Volume 38, Number 6 (2010), 2258-2294.

Dates
First available in Project Euclid: 24 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1285334206

Digital Object Identifier
doi:10.1214/10-AOP537

Mathematical Reviews number (MathSciNet)
MR2683630

Zentralblatt MATH identifier
1210.60109

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Random walk in random environment current fluctuations central limit theorem

Citation

Peterson, Jonathon; Seppäläinen, Timo. Current fluctuations of a system of one-dimensional random walks in random environment. Ann. Probab. 38 (2010), no. 6, 2258--2294. doi:10.1214/10-AOP537. https://projecteuclid.org/euclid.aop/1285334206


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