Monotonicity of functionals of random polytopes

2017/06/26 by Beermann, Mareen, Reitzner, Matthias
#60D05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1706.08342

Abstract

The convex hull P_n of a Gaussian sample X₁,...,X_n in R^d is a Gaussian polytope. We prove that the expected number of facets E f_d-1 (P_n) is monotonically increasing in n. Furthermore we prove this for random polytopes generated by uniformly distributed points in a d-dimensional ball.

Related

• Monotonicity of expected f-vectors for projections of regular\n polytopes
• Estranged facets and k-facets of Gaussian random point sets
• Central limit theorems for Gaussian polytopes
• Random polytopes in convex bodies: Bridging the gap between extremal containers
• Facets of high-dimensional Gaussian polytopes