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The Dimension of the Frontier of Planar Brownian Motion


 
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1. Title Title of document The Dimension of the Frontier of Planar Brownian Motion
 
2. Creator Author's name, affiliation, country Gregory F. Lawler; Duke University
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Brownian motion, Hausdorff dimension, frontier, random fractals
 
3. Subject Subject classification 60J65
 
4. Description Abstract Let $B$ be a two dimensional Brownian motion and let the frontier of $B[0,1]$ be defined as the set of all points in $B[0,1]$ that are in the closure of the unbounded connected component of its complement. We prove that the Hausdorff dimension of the frontier equals $2(1 - \alpha)$ where $\alpha$ is an exponent for Brownian motion called the two-sided disconnection exponent. In particular, using an estimate on $\alpha$ due to Werner, the Hausdorff dimension is greater than $1.015$.
 
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7. Date (YYYY-MM-DD) 1996-03-10
 
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/975
 
10. Identifier Digital Object Identifier 10.1214/ECP.v1-975
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 1
 
12. Language English=en en
 
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