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A $0$-$1$ law for vertex-reinforced random walks on $\mathbb{Z}$ with weight of order $k^\alpha$, $\alpha\in[0,1/2)$


 
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1. Title Title of document A $0$-$1$ law for vertex-reinforced random walks on $\mathbb{Z}$ with weight of order $k^\alpha$, $\alpha\in[0,1/2)$
 
2. Creator Author's name, affiliation, country Bruno Schapira; Université Paris Sud 11 (Orsay); France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Self-interacting random walk; Reinforced random walk; $0$-$1$ law
 
3. Subject Subject classification 60F20; 60K35
 
4. Description Abstract We prove that Vertex Reinforced Random Walk on $\mathbb{Z}$ with weight  of order $k^\alpha$, with $\alpha\in [0,1/2)$, is either almost surely recurrent or almost surely transient.  This improves a previous result of Volkov who showed that the set of sites which are visited infinitely often was a.s. either empty or infinite.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR Randymeca; ANR MEMEMO2
 
7. Date (YYYY-MM-DD) 2012-06-13
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2084
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-2084
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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