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


 
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1. Title Title of document Systems of One-Dimensional Random Walks in a Common Random Environment.
 
2. Creator Author's name, affiliation, country Jonathon Peterson; Cornell University; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random walk in random environment; hydrodynamic limit; large deviations
 
3. Subject Subject classification 60K37; 60F10; 60K35
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF. Institut Mittag-Leffler.
 
7. Date (YYYY-MM-DD) 2010-07-06
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/784
 
10. Identifier Digital Object Identifier 10.1214/EJP.v15-784
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 15
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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