D. G. Kendall conjecture concerning the planar Crofton cell and its Browian counterpart
成果类型：
Article
署名作者：
Goldman, PA
署名单位：
Universite Claude Bernard Lyon 1
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1998
页码：
1727-1750
关键词：
摘要：
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.