Thomas Godland

most citedRandom cones in high dimensions I: Donoho-Tanner and Cover-Efron cones

8 citations · 8 across the 6 of their papers we have counts for

collaborators

8 papers

math.PR2021

Beta-star polytopes and hyperbolic stochastic geometry

Thomas Godland, Zakhar Kabluchko, Christoph Thäle

Motivated by problems of hyperbolic stochastic geometry we introduce and study the class of beta-star polytopes. A beta-star polytope is defined as the convex hull of an inhomogene…

math.PR2021

Random cones in high dimensions II: Weyl cones

Thomas Godland, Zakhar Kabluchko, Christoph Thäle

We consider two models of random cones together with their duals. Let $Y_{1}, \dots, Y_{n}$ be independent and identically distributed random vectors in $R^{d}$ whose distribution…

math.PR2021

Positive hulls of random walks and bridges

Thomas Godland, Zakhar Kabluchko

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 t…

math.PR2020★ 8 cited

Random cones in high dimensions I: Donoho-Tanner and Cover-Efron cones

Thomas Godland, Zakhar Kabluchko, Christoph Thaele

Two models of random cones in high dimensions are considered, together with their duals. The Donoho-Tanner random cone $D_{n, d}$ can be defined as the positive hull of $n$ independ…

math.MG2020

Projections and angle sums of belt polytopes and permutohedra

Thomas Godland, Zakhar Kabluchko

Let $P \subset R^{n}$ be a belt polytope, that is a polytope whose normal fan coincides with the fan of some hyperplane arrangement $A$ . Also, let $G:\mathbb R^n\to\m…

math.PR2020

Angle sums of random polytopes

Thomas Godland, Zakhar Kabluchko, Dmitry Zaporozhets

For two families of random polytopes we compute explicitly the expected sums of the conic intrinsic volumes and the Grassmann angles at all faces of any given dimension of the poly…

math.PR2020

Angle sums of Schläfli orthoschemes

Thomas Godland, Zakhar Kabluchko

We consider the simplices $K_{n}^{A} = {x \in R^{n + 1} : x_{1} \geq x_{2} \geq \dots \geq x_{n + 1}, x_{1} - x_{n + 1} \leq 1, x_{1} + \dots + x_{n + 1} = 0}$ and $$ K_n^B=\{x\in\mathbb{R}^n:1\ge x_1\ge x_2…

math.PR2020

Conic intrinsic volumes of Weyl chambers

Thomas Godland, Zakhar Kabluchko

We give a new, direct proof of the formulas for the conic intrinsic volumes of the Weyl chambers of types $A_{n - 1}, B_{n}$ and $D_{n}$ . These formulas express the conic intrinsic volum…