Electronic Journal of Probability

Systems of One-Dimensional Random Walks in a Common Random Environment.

Jonathon Peterson

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 32, 1024-1040.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819817

Digital Object Identifier
doi:10.1214/EJP.v15-784

Mathematical Reviews number (MathSciNet)
MR2659756

Zentralblatt MATH identifier
1225.60159

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60F10: Large deviations 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Random walk in random environment hydrodynamic limit large deviations

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Peterson, Jonathon. Systems of One-Dimensional Random Walks in a Common Random Environment. Electron. J. Probab. 15 (2010), paper no. 32, 1024--1040. doi:10.1214/EJP.v15-784. https://projecteuclid.org/euclid.ejp/1464819817


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