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Cut Times for Simple Random Walk


 
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1. Title Title of document Cut Times for Simple Random Walk
 
2. Creator Author's name, affiliation, country Gregory F. Lawler; Duke University and Cornell University
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Random walk, cut points, intersection exponent
 
3. Subject Subject classification 60J15
 
4. Description Abstract Let $S(n)$ be a simple random walk taking values in $Z^d$. A time $n$ is called a cut time if
\[ S[0,n] \cap S[n+1,\infty) = \emptyset . \]
We show that in three dimensions the number of cut times less than $n$ grows like $n^{1 - \zeta}$ where $\zeta = \zeta_d$ is the intersection exponent. As part of the proof we show that in two or three dimensions
\[ P(S[0,n] \cap S[n+1,2n] = \emptyset ) \sim n^{-\zeta}, \]
where $\sim$ denotes that each side is bounded by a constant times the other side.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 1996-10-19
 
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/13
 
10. Identifier Digital Object Identifier 10.1214/EJP.v1-13
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 1
 
12. Language English=en en
 
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