Philipp Schange

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math.PR2026

Angles and volumes of simplices, boxes, and crosspolytopes in constant curvature

Zakhar Kabluchko, Philipp Schange

We determine, up to isometry, the Riemannian tangent and normal cones at arbitrary faces of boxes, acute orthocentric simplices, rectangular simplices, and asymmetric crosspolytope…

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 $β_{i} \geq - 1$ : if $β_{i} > - 1$ …