Stability results for the volume of random simplices

2010/05/27 by Gergely Ambrus, Ambrus, Gergely, Károly J. Böröczky +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.MG

paper · pdf · doi:10.48550/arxiv.1005.5024

26 pages

openalex publication_date 2010/05/27 · arxiv created 2010/06/02 · arxiv updated 2010/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

It is known that for a convex body K in R^d of volume one, the expected volume of random simplices in K is minimised if K is an ellipsoid, and for d = 2, maximised if K is a triangle. Here we provide corresponding stability estimates.

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