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Hausdorff Dimension of Cut Points for Brownian Motion


 
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1. Title Title of document Hausdorff Dimension of Cut Points for Brownian Motion
 
2. Creator Author's name, affiliation, country Gregory F. Lawler; Duke University and Cornell University
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Brownian motion,Hausdorff dimension, cut points, intersection exponent
 
3. Subject Subject classification 60J65
 
4. Description Abstract Let $B$ be a Brownian motion in $R^d$, $d=2,3$. A time $t\in [0,1]$ is called a cut time for $B[0,1]$ if $B[0,t) \cap B(t,1] = \emptyset$. We show that the Hausdorff dimension of the set of cut times equals $1 - \zeta$, where $\zeta = \zeta_d$ is the intersection exponent. The theorem, combined with known estimates on $\zeta_3$, shows that the percolation dimension of Brownian motion (the minimal Hausdorff dimension of a subpath of a Brownian path) is strictly greater than one in $R^3$.
 
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7. Date (YYYY-MM-DD) 1995-11-08
 
8. Type Status & genre Peer-reviewed Article
 
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9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2
 
10. Identifier Digital Object Identifier 10.1214/EJP.v1-2
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 1
 
12. Language English=en en
 
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