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 Electronic Journal of Probability > Vol. 1 (1996) > Paper 2 open journal systems 


Hausdorff Dimension of Cut Points for Brownian Motion

Gregory F. Lawler, Duke University and Cornell University


Abstract
Let $B$ be a Brownian motion in $R^d$, $d=2,3$. A time $tin [0,1]$ 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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Pages: 1-20

Published on: November 8, 1995
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Electronic Journal of Probability. ISSN: 1083-6489