We study the probability distribution of the area and the number of vertices of random polygons in a convex set K⊂ℝ2. The novel aspect of our approach is that it yields uniform estimates for all convex sets K⊂ℝ2 without imposing any regularity conditions on the boundary ∂K. Our main result is a central limit theorem for both the area and the number of vertices, settling a well-known conjecture in the field. We also obtain asymptotic results relating the growth of the expectation and variance of these two functionals.
Publié le : 2011-05-15
Classification:
Random polygons,
central limit theorem,
52A22,
60D05,
60F05
@article{1300281727,
author = {Pardon, John},
title = {Central limit theorems for random polygons in an arbitrary convex set},
journal = {Ann. Probab.},
volume = {39},
number = {1},
year = {2011},
pages = { 881-903},
language = {en},
url = {http://dml.mathdoc.fr/item/1300281727}
}
Pardon, John. Central limit theorems for random polygons in an arbitrary convex set. Ann. Probab., Tome 39 (2011) no. 1, pp. 881-903. http://gdmltest.u-ga.fr/item/1300281727/