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2010 Systems of One-Dimensional Random Walks in a Common Random Environment.
Jonathon Peterson
Author Affiliations +
Electron. J. Probab. 15: 1024-1040 (2010). DOI: 10.1214/EJP.v15-784

Abstract

We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed. We give upper bounds on the quenched probability that at least one of the random walks started in an interval has experience a large deviation slowdown. This leads to both a uniform law of large numbers and a hydrodynamic limit for the system of random walks. We also identify a family of distributions on the configuration of particles (parameterized by particle density) which are stationary under the (quenched) dynamics of the random walks and show that these are the limiting distributions for the system when started from a certain natural collection of distributions.

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Jonathon Peterson. "Systems of One-Dimensional Random Walks in a Common Random Environment.." Electron. J. Probab. 15 1024 - 1040, 2010. https://doi.org/10.1214/EJP.v15-784

Information

Accepted: 6 July 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1225.60159
MathSciNet: MR2659756
Digital Object Identifier: 10.1214/EJP.v15-784

Subjects:
Primary: 60K37
Secondary: 60F10, 60K35

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Vol.15 • 2010
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