Approximation of smooth convex bodies by random circumscribed polytopes

• 成果类型: Article
• 署名作者: Boroczky, K; Reitzner, M
• 署名单位: HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of Freiburg
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2004
• 页码: 239-273
• 关键词: delone triangulation numbers; stepwise approximation; ball

摘要

Choose n independent random points on the boundary of a convex body K subset of R-d. The intersection of the supporting halfspaces at these random points is a random convex polyhedron. The expectations of its volume, its surface area and its mean width are investigated. In the case that the boundary of K is sufficiently smooth, asymptotic expansions as n --> infinity are derived even in the case when the curvature is allowed to be zero. We compare our results to the analogous results for best approximating polytopes.