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Self-repelling random walk with directed edges on Z


 
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1. Title Title of document Self-repelling random walk with directed edges on Z
 
2. Creator Author's name, affiliation, country Balint Veto; Budapest University of Technology
 
2. Creator Author's name, affiliation, country Balint Toth; Budapest University of Technology
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random walks with long memory, self-repelling, one dimension, oriented edges, local time, Ray-Knight-theory, coupling
 
3. Subject Subject classification 60G50, 82B41, 82C41
 
4. Description Abstract We consider a variant of self-repelling random walk on the integer lattice Z where the self-repellence is defined in terms of the local time on oriented edges. The long-time asymptotic scaling of this walk is surprisingly different from the asymptotics of the similar process with self-repellence defined in terms of local time on unoriented edges. We prove limit theorems for the local time process and for the position of the random walker. The main ingredient is a Ray-Knight-type of approach. At the end of the paper, we also present some computer simulations which show the strange scaling behaviour of the walk considered.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2008-10-30
 
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/570
 
10. Identifier Digital Object Identifier 10.1214/EJP.v13-570
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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