Random approximation of convex bodies in Hausdorff metric

Autor:	Prochno, Joscha, Schütt, Carsten, Sonnleitner, Mathias, Werner, Elisabeth M.
Rok vydání:	2024
Předmět:	Mathematics - Metric Geometry Mathematics - Probability 52A22 52A27 60D05
Druh dokumentu:	Working Paper
Popis:	While there is extensive literature on approximation, deterministic as well as random, of general convex bodies $K$ in the symmetric difference metric, or other metrics arising from intrinsic volumes, very little is known for corresponding random results in the Hausdorff distance when the approximant $K_n$ is given by the convex hull of $n$ independent random points chosen uniformly on the boundary or in the interior of $K$. When $K$ is a polygon and the points are chosen on its boundary, we determine the exact limiting behavior of the expected Hausdorff distance between a polygon as $n\to\infty$. From this we derive the behavior of the asymptotic constant for a regular polygon in the number of vertices. Comment: 17 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.02870 Zobrazit plný text záznamu View this record from Arxiv