The Hausdorff Dimension of the Double Points on the Brownian Frontier

Richard Kiefer () and Peter Mörters ()
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Richard Kiefer: RWE Power AG
Peter Mörters: University of Bath

Journal of Theoretical Probability, 2010, vol. 23, issue 2, 605-623

Abstract: Abstract The frontier of a planar Brownian motion is the boundary of the unbounded component of the complement of its range. In this paper, we find the Hausdorff dimension of the set of double points on the frontier.

Keywords: Brownian motion; Self-intersections; Double points; Frontier; Outer boundary; Disconnection exponent; Mandelbrot conjecture; Hausdorff dimension; 60J65; 60G17 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-009-0262-2

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