Convex hulls of random walks: expected number of faces and face probabilities

DOI10.1016/j.aim.2017.09.002zbMath1377.52007arXiv1612.00249OpenAlexW2560399282MaRDI QIDQ2411338

Dmitry Zaporozhets, Zakhar Kabluchko, Vladislav V. Vysotsky

Publication date: 20 October 2017

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.00249

zbMATH Keywords

exchangeabilityrandom polytopehyperplane arrangementWeyl chamberabsorption probabilityconvex hull of random walk

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Extreme value theory; extremal stochastic processes (60G70) Sums of independent random variables; random walks (60G50) (n)-dimensional polytopes (52B11) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Random convex sets and integral geometry (aspects of convex geometry) (52A22) Exchangeability for stochastic processes (60G09)

Related Items (12)

Positive hulls of random walks and bridges ⋮ Mean area of the convex hull of a run and tumble particle in two dimensions ⋮ Statistics of the maximum and the convex hull of a Brownian motion in confined geometries ⋮ Conic intrinsic volumes of Weyl chambers ⋮ Angle sums of Schläfli orthoschemes ⋮ Angle sums of random polytopes ⋮ The convex hull of a planar random walk: perimeter, diameter, and shape ⋮ The convex hull of the run-and-tumble particle in a plane ⋮ Dini derivatives and regularity for exchangeable increment processes ⋮ Conical tessellations associated with Weyl chambers ⋮ Convex hulls of stable random walks ⋮ Lah distribution: Stirling numbers, records on compositions, and convex hulls of high-dimensional random walks

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