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July, 1989 Cut Points on Brownian Paths
Krzysztof Burdzy
Ann. Probab. 17(3): 1012-1036 (July, 1989). DOI: 10.1214/aop/1176991254

Abstract

Let $X$ be a standard two-dimensional Brownian motion. There exists a.s. $t \in (0, 1)$ such that $X(\lbrack 0, t)) \cap X((t, 1 \rbrack) = \varnothing$. It follows that $X(\lbrack 0, 1 \rbrack)$ is not homeomorphic to the Sierpinski carpet a.s.

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Krzysztof Burdzy. "Cut Points on Brownian Paths." Ann. Probab. 17 (3) 1012 - 1036, July, 1989. https://doi.org/10.1214/aop/1176991254

Information

Published: July, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0691.60069
MathSciNet: MR1009442
Digital Object Identifier: 10.1214/aop/1176991254

Subjects:
Primary: 60J65
Secondary: 60G17

Keywords: Brownian motion , cut points , Fractal , Random fractal

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 3 • July, 1989
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