Thomas Godland

collaborators

3 papers

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.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…