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.
Publié le : 1998-10-14
Classification:
Poisson line process,
Crofton cell,
random polygons,
perimeter of the convex hull of Brownian motion,
eigenvalues,
60D05,
60J65,
35P20,
52A22,
60F10
@article{1022855880,
author = {Goldman, Andr\'e},
title = {Sur une conjecture de D. G. Kendall concernant la cellule de
Crofton du plan et sur sa contrepartie brownienne},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 1727-1750},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855880}
}
Goldman, André. Sur une conjecture de D. G. Kendall concernant la cellule de
Crofton du plan et sur sa contrepartie brownienne. Ann. Probab., Tome 26 (1998) no. 1, pp. 1727-1750. http://gdmltest.u-ga.fr/item/1022855880/