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Sub-ballistic random walk in Dirichlet environment


 
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1. Title Title of document Sub-ballistic random walk in Dirichlet environment
 
2. Creator Author's name, affiliation, country Élodie Bouchet; Université de Lyon; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random walk in random environment; Dirichlet distribution; Reinforced random walks; Invariant measure viewed from the particle
 
3. Subject Subject classification primary 60K37; 60K35
 
4. Description Abstract

We consider random walks in Dirichlet environment (RWDE) on $\mathbb{Z} ^d$, for $d \geq 3$, in the sub-ballistic case. We associate to any parameter $ (\alpha_1, \dots, \alpha _{2d}) $ of the Dirichlet law a time-change to accelerate the walk. We prove that the continuous-time accelerated walk has an absolutely continuous invariant probability measure for the environment viewed from the particle. This allows to characterize directional transience for the initial RWDE. It solves as a corollary the problem of Kalikow's $0-1$ law in the Dirichlet case in any dimension. Furthermore, we find the polynomial order of the magnitude of the original walk's displacement.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR project MEMEMO2
 
7. Date (YYYY-MM-DD) 2013-05-25
 
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/2109
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2109
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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