Open Access
November 2010 Current fluctuations of a system of one-dimensional random walks in random environment
Jonathon Peterson, Timo Seppäläinen
Ann. Probab. 38(6): 2258-2294 (November 2010). DOI: 10.1214/10-AOP537


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.


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Jonathon Peterson. Timo Seppäläinen. "Current fluctuations of a system of one-dimensional random walks in random environment." Ann. Probab. 38 (6) 2258 - 2294, November 2010.


Published: November 2010
First available in Project Euclid: 24 September 2010

zbMATH: 1210.60109
MathSciNet: MR2683630
Digital Object Identifier: 10.1214/10-AOP537

Primary: 60K37
Secondary: 60K35

Keywords: central limit theorem , current fluctuations , Random walk in random environment

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 6 • November 2010
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