题目：Approximation of Convex Bodies in Hausdorff Distance by Random Polytopes

报告人：Elisabeth Werner（Case Western Reserve University）

地点：致远楼101室

时间：2024年11月17日 10:00-11:00

摘要: While there is extensive literature on approximation, deterministic as well as random,  of general convex bodies in the symmetric difference metric, or other metrics coming from intrinsic volumes, very little is known  for corresponding random results in the Hausdorff distance.

For a polygon Q in the plane, the convex hull of n points chosen at random on the boundary of Q gives a random polygon Q_n. We determine the exact limiting behavior of the expected Hausdorff distance between Q and a random polygon Q_n as the number n of points chosen on the boundary of Q goes to infinity.

Based on joint work with J. Prochno, C. Schuett and M. Sonnleitner.

All are welcome!