Zakhar Kabluchko

activity

20242026

collaborators

19 papers

math.PR2026

Intrinsic volumes of $ℓ_{p}$ -balls and a continuum of Maxwell--PoincarÃ©--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 $I^_{i}^{2} \geq - 1$ : if $Î²_i>-…

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 $I^»$ -Geodesic Hyperplanes

Zakhar Kabluchko, Vanessa Mattutat, Christoph Thaele

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

math.PR2026

A refinement of the Sylvester problem: Probabilities of combinatorial types

Zakhar Kabluchko, Hugo Panzo

Let $X_{1}, \dots, X_{d + 2}$ be random points in $R^{d}$ . The classical Sylvester problem asks to determine the probability that the convex hull of these points, denoted by $P:=…

math.PR2026

Zero distribution of multiplicative Hermite and Laguerre polynomials

Zakhar Kabluchko

It is well-known that, as $n \to \infty$ , the zero distribution of the $n$ -th Hermite polynomial converges to the semicircular law (the free normal distribution), while the zero dist…

Intrinsic volumes of ℓp​-balls and a continuum of Maxwell--PoincarÃ©--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 I^»-Geodesic Hyperplanes

A refinement of the Sylvester problem: Probabilities of combinatorial types

Zero distribution of multiplicative Hermite and Laguerre polynomials

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

Seeing Through Hyperbolic Space: Visibility for $I^»$ -Geodesic Hyperplanes