Positive hulls of random walks and bridges

Thomas Godland; Zakhar Kabluchko

Positive hulls of random walks and bridges

Probability 2022-01-31 v2 Metric Geometry

Authors: Thomas Godland , Zakhar Kabluchko

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.

Keywords

random walks random bridges positive hulls random convex cones stirling numbers quermassintegrals geometric functionals

Cite

@article{arxiv.2104.05542,
  title  = {Positive hulls of random walks and bridges},
  author = {Thomas Godland and Zakhar Kabluchko},
  journal= {arXiv preprint arXiv:2104.05542},
  year   = {2022}
}

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34 pages

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