Zakhar Kabluchko

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20242026

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14 papers · 1 filter

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…

math.PR2026

First passage times for decoupled random walks

Alexander Iksanov, Zakhar Kabluchko, Vitali Wachtel

Motivated by a connection to the infinite Ginibre point process, decoupled random walks were introduced in a recent article Alsmeyer, Iksanov and Kabluchko (2025). The decoupled ra…

math.PR2025

On the distribution patterns of zeros for random polynomials with regularly varying coefficients

Zakhar Kabluchko, Boris Khoruzhenko, Alexander Marynych

This paper investigates asymptotic distribution of complex zeros of random polynomials $P_{n} (z) := \sum_{k = 0}^{n} b (k) ξ_{k} z^{k}$ , as $n \to \infty$ , where $b$ is a regularly varying functi…

math.PR2025

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…

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

First passage times for decoupled random walks

On the distribution patterns of zeros for random polynomials with regularly varying coefficients

Zero distribution of multiplicative Hermite and Laguerre polynomials

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