Philipp Schange

collaborators

3 papers

math.PR2026

Expected hyperbolic volumes of random beta polytopes

Zakhar Kabluchko, Philipp Schange

Let $X_{1}, \dots, X_{n}$ be independent random points in the closed unit ball of $R^{d}$ . Assume that each $X_{i}$ has a beta distribution with parameter $I^_{i}^{2} \geq - 1$ : if $Î²_i>-…

math.MG2025

Volumes of Regular Hyperbolic Simplices

Zakhar Kabluchko, Philipp Schange

We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.

math.MG2025

Angles of orthocentric simplices

Zakhar Kabluchko, Philipp Schange

A $d$ -dimensional simplex in Euclidean space is called orthocentric if all of its altitudes intersect at a single point, referred to as the orthocenter. We explicitly compute the i…