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July 2005 The multifractal spectrum of Brownian intersection local times
Achim Klenke, Peter Mörters
Ann. Probab. 33(4): 1255-1301 (July 2005). DOI: 10.1214/009117905000000116

Abstract

Let ℓ be the projected intersection local time of two independent Brownian paths in ℝd for d=2,3. We determine the lower tail of the random variable $\ell(\mathbb {U})$, where $\mathbb {U}$ is the unit ball. The answer is given in terms of intersection exponents, which are explicitly known in the case of planar Brownian motion. We use this result to obtain the multifractal spectrum, or spectrum of thin points, for the intersection local times.

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Achim Klenke. Peter Mörters. "The multifractal spectrum of Brownian intersection local times." Ann. Probab. 33 (4) 1255 - 1301, July 2005. https://doi.org/10.1214/009117905000000116

Information

Published: July 2005
First available in Project Euclid: 1 July 2005

zbMATH: 1080.60078
MathSciNet: MR2150189
Digital Object Identifier: 10.1214/009117905000000116

Subjects:
Primary: 60G17 , 60J55 , 60J65

Keywords: Brownian motion , Hausdorff dimension spectrum , Hausdorff measure , intersection exponent , Intersection local time , intersection of Brownian paths , lower tail asymptotics , multifractal spectrum , thin points , Wiener sausage

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 4 • July 2005
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