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Two-sided random walks conditioned to have no intersections


 
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1. Title Title of document Two-sided random walks conditioned to have no intersections
 
2. Creator Author's name, affiliation, country Daisuke Shiraishi; Kyoto University; Japan
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random walks; Cut points; Invariant measure
 
3. Subject Subject classification 05C81
 
4. Description Abstract Let $S^{1},S^{2}$ be independent simple random walks in $\mathbb{Z}^{d}$ ($d=2,3$) started at the origin. We construct two-sided random walk paths conditioned that $S^{1}[0,\infty ) \cap S^{2}[1, \infty ) = \emptyset$ by showing the existence of the following limit:
\begin{equation*}
\lim _{n \rightarrow \infty } P ( \cdot   |  S^{1}[0, \tau ^{1} ( n) ] \cap S^{2}[1, \tau ^{2}(n) ] = \emptyset ),
\end{equation*}
where $\tau^{i}(n) = \inf \{ k \ge 0 : |S^{i} (k) | \ge n \}$. Moreover, we give upper bounds of the rate of the convergence. These are discrete analogues of results for Brownian motion obtained by Lawler.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) JSPS Research Fellowships
 
7. Date (YYYY-MM-DD) 2012-02-28
 
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/1742
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1742
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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