Positive hulls of random walks and bridges

2021/04/12 by Godland, Thomas, Kabluchko, Zakhar
#51F15 #52A55 #52B05 #60D05. Secondary: 11B73 #FOS: Mathematics #Metric Geometry (math.MG) #Primary: 52A22 #Probability (math.PR)

paper · doi:10.48550/arxiv.2104.05542

Abstract

We study random convex cones defned as positive hulls of d-dimensional random walks and bridges. We compute expectations of various geometric functionals of these cones such as the number of k-dimensional faces and the sums of conic quermassintegrals of their k-dimensional faces. These expectations are expressed in terms of Stirling numbers of both kinds and their B-analogues.

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