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Percolation Dimension of Brownian Motion in $R^3$


 
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1. Title Title of document Percolation Dimension of Brownian Motion in $R^3$
 
2. Creator Author's name, affiliation, country Chad Fargason; Duke University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Percolation dimension, boundary dimension, intersection exponent
 
3. Subject Subject classification 60J65.
 
4. Description Abstract Let $B(t)$ be a Brownian motion in $R^3$. A subpath of the Brownian path $B[0,1]$ is a continuous curve $\gamma(t)$, where $\gamma[0,1] \subseteq B[0,1]$ , $\gamma(0) = B(0)$, and $\gamma(1) = B(1)$. It is well-known that any subset $S$ of a Brownian path must have Hausdorff dimension $\text{dim} (S) \leq 2.$ This paper proves that with probability one there exist subpaths of $B[0,1]$ with Hausdorff dimension strictly less than 2. Thus the percolation dimension of Brownian motion in $R^3$ is strictly less than 2.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 1998-02-27
 
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/993
 
10. Identifier Digital Object Identifier 10.1214/ECP.v3-993
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 3
 
12. Language English=en
 
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