Zakhar Kabluchko

activity

20122026

most citedRandom determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields

1 citations · 1 across the 22 of their papers we have counts for

collaborators

23 papers

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 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

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…

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.NT2025

Arithmetic sensitivity of cumulant growth in lacunary sums: transcendental versus algebraic ratio limits

Christoph Aistleitner, Zakhar Kabluchko, Joscha Prochno

We study the asymptotic behavior of cumulants of lacunary trigonometric sums $S_{n} (ω) := \sum_{k = 1}^{n} cos (2 π a_{k} ω)$ , $ω \in [0, 1]$ , and show that cumulant growth is highly sensitiv…

math.PR2025

Zeros of polynomial powers under the heat flow

Antonia Höfert, Jonas Jalowy, Zakhar Kabluchko

We study the zero evolution of high powers of polynomials under the heat flow. For any fixed polynomial $P (z)$ , we prove that the empirical zero distribution of its heat-evolved $n…

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…

math.CA2025

Zeros and exponential profiles of polynomials II: Examples

Jonas Jalowy, Zakhar Kabluchko, Alexander Marynych

In [Jalowy, Kabluchko, Marynych, arXiv:2504.11593v1, 2025], the authors discuss a user-friendly approach to determine the limiting empirical zero distribution of a sequence of real…

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.PR2025

On the shape of the typical Poisson-Voronoi cell in high dimensions

Matthias Irlbeck, Zakhar Kabluchko, Tobias Müller

We study the typical cell of the Poisson-Voronoi tessellation. We show that when divided by the $d$ -th root of the intensity parameter $λ$ of the Poisson process times the volume o…

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…

math.PR2025

Zeros and exponential profiles of polynomials I: Limit distributions, finite free convolutions and repeated differentiation

Jonas Jalowy, Zakhar Kabluchko, Alexander Marynych

Given a sequence of polynomials $(P_{n})_{n \in N}$ with only nonpositive zeros, the aim of this article is to present a user-friendly approach for determining the limiting…

math.PR2025

Beta Polytopes and Beta Cones: An Exactly Solvable Model in Geometric Probability

Zakhar Kabluchko, David Albert Steigenberger

Let $X_{1}, \dots, X_{n}$ be independent random points in the unit ball of $R^{d}$ such that $X_{i}$ follows a beta distribution with the density proportional to $(1-\|x\|^2)^{β_i}…

math.PR2025

Almost periodic stochastic processes with applications to analytic number theory

Alexander Iksanov, Zakhar Kabluchko, Alexander Marynych

A classical fact of the theory of almost periodic functions is the existence of their asymptotic distributions. In probabilistic terms, this means that if $f$ is a Besicovitch almo…

math.PR2025

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.PR2025

Sylvester's problem for beta-type distributions

Anna Gusakova, Zakhar Kabluchko

Consider $d + 2$ i.i.d. random points $X_{1}, \dots, X_{d + 2}$ in $R^{d}$ . In this note, we compute the probability that their convex hull is a simplex focusing on three specific…

math.PR2024

Strange shadows of $ℓ_{p}$ -balls

Zakhar Kabluchko, Mathias Sonnleitner

We prove a large deviations principle for orthogonal projections of the unit ball $B_{p}^{n}$ of $ℓ_{p}^{n}$ onto a random $k$ -dimensional linear subspace of $R^{n}$ as…

math.PR2024

Propagation of chaos and residual dependence in Gibbs measures on finite sets

Jonas Jalowy, Zakhar Kabluchko, Matthias Löwe

We compare a mean-field Gibbs distribution on a finite state space on $N$ spins to that of an explicit simple mixture of product measures. This illustrates the situation beyond the…

math.PR2012★ 1 cited

Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields

Zakhar Kabluchko, Dmitry Zaporozhets

Consider a $d \times d$ matrix $M$ whose rows are independent centered non-degenerate Gaussian vectors $ξ_{1}, ..., ξ_{d}$ with covariance matrices $Σ_{1}, ..., Σ_{d}$ . Denote by $\mathcal{E}_i…

Coverage probability of the planar Brownian convex hull

Angles and volumes of simplices, boxes, and crosspolytopes in 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

First passage times for decoupled random walks

Arithmetic sensitivity of cumulant growth in lacunary sums: transcendental versus algebraic ratio limits

Zeros of polynomial powers under the heat flow

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

Zero distribution of multiplicative Hermite and Laguerre polynomials

Zeros and exponential profiles of polynomials II: Examples

Volumes of Regular Hyperbolic Simplices

On the shape of the typical Poisson-Voronoi cell in high dimensions

Angles of orthocentric simplices

Zeros and exponential profiles of polynomials I: Limit distributions, finite free convolutions and repeated differentiation

Beta Polytopes and Beta Cones: An Exactly Solvable Model in Geometric Probability

Almost periodic stochastic processes with applications to analytic number theory

A refinement of the Sylvester problem: Probabilities of combinatorial types

Sylvester's problem for beta-type distributions

Strange shadows of ℓp​-balls

Propagation of chaos and residual dependence in Gibbs measures on finite sets

Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields

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

Strange shadows of $ℓ_{p}$ -balls