Random zonotopes and valuations

2022/02/14 by Schneider, Rolf
#60D05 #FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.2202.06774

Abstract

We define a random zonotope in Euclidean space, by adding finitely many random segments, which are independently and identically distributed. For this random polytope, we determine, under a mild assumption on the distribution, the expectations of the intrinsic volumes, more generally, the expectations of suitable valuations. We also prove a central limit theorem for a valuation evaluated at these random zonotopes.

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