Zakhar Kabluchko

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20242026

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7 papers · 2 filters

math.PR2026

Coverage probability of the planar Brownian convex hull

Zakhar Kabluchko

Let $K$ be the convex hull of a planar Brownian motion up to time $1$ . We explicitly determine the probability that $K$ contains a prescribed point $z\in\mathbb R…

math.PR2026

Angles and volumes of regular polytopes in geometries of constant curvature

Zakhar Kabluchko, Philipp Schange

We derive closed-form expressions for the internal and external angles of $d$ -dimensional cubes, regular simplices and regular crosspolytopes in geometries of constant sectional cu…

math.PR2026

Intrinsic volumes of $ℓ_{p}$ -balls and a continuum of Maxwell--Poincaré--Borel laws for their curvature measures

Zakhar Kabluchko, Alexander Marynych, Joscha Prochno

For $p > 1$ , we derive explicit formulas for the intrinsic volumes $V_{0} (B_{p}^{n}), \dots, V_{n - 1} (B_{p}^{n})$ of the $n$ -dimensional $ℓ_{p}$ -balls $$ \mathbb B_p^n = \{x\in\m…

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 $β_{i} > - 1$ …

math.PR2026

Random Polyhedral Cones I: Distributional Results via Gale Duality

Zakhar Kabluchko

Let $U_{1}, \dots, U_{n}$ be independent random vectors uniformly distributed on the unit sphere $S^{d - 1} \subseteq R^{d}$ , where $n \geq d$ , and consider the random polyhedra…

math.PR2026

Seeing Through Hyperbolic Space: Visibility for $λ$ -Geodesic Hyperplanes

Zakhar Kabluchko, Vanessa Mattutat, Christoph Thaele

We study visibility from a fixed point in the presence of a Poisson process of $λ$ --geodesic hyperplanes in a $d$ -dimensional hyperbolic space. The family of $λ$ --geodesic hyperpla…

Coverage probability of the planar Brownian convex hull

Angles and volumes of regular polytopes in geometries of constant curvature

Intrinsic volumes of ℓp​-balls and a continuum of Maxwell--Poincaré--Borel laws for their curvature measures

Expected hyperbolic volumes of random beta polytopes

Random Polyhedral Cones I: Distributional Results via Gale Duality

Seeing Through Hyperbolic Space: Visibility for λ-Geodesic Hyperplanes

Intrinsic volumes of $ℓ_{p}$ -balls and a continuum of Maxwell--Poincaré--Borel laws for their curvature measures

Seeing Through Hyperbolic Space: Visibility for $λ$ -Geodesic Hyperplanes