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October 1998 Sur une conjecture de D. G. Kendall concernant la cellule de Crofton du plan et sur sa contrepartie brownienne
André Goldman
Ann. Probab. 26(4): 1727-1750 (October 1998). DOI: 10.1214/aop/1022855880

Abstract

In connection with a conjecture stated by D. G. Kendall in the forties, we describe the asymptotic behavior of the distribution function of the area of the planar Crofton cell. We deduce from this (in support of his conjecture) that expressed in terms of eigenvalues, the large Crofton cells are nearly circular. We obtain also the asymptotic behavior of the Laplace transform of the law of the perimeter of the convex hull of planar Brownian motion run until time 1. This last result implies that the small convex hulls of Brownian motion are nearly circular.

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André Goldman. "Sur une conjecture de D. G. Kendall concernant la cellule de Crofton du plan et sur sa contrepartie brownienne." Ann. Probab. 26 (4) 1727 - 1750, October 1998. https://doi.org/10.1214/aop/1022855880

Information

Published: October 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0936.60009
MathSciNet: MR1675067
Digital Object Identifier: 10.1214/aop/1022855880

Subjects:
Primary: 60D05, 60J65
Secondary: 35P20, 52A22, 60F10

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 4 • October 1998
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