A. Gusakova

activity

20192026

most citedSharp inequalities for the mean distance of random points in convex bodies

4 citations · 8 across the 20 of their papers we have counts for

collaborators

23 papers

math.PR2026

Functional central limit theorems for Laguerre tessellations

Chinmoy Bhattacharjee, Anna Gusakova, Christian Hirsch

We study empirical processes of observable extreme generators in stationary Poisson-Laguerre tessellations, with each generator weighted either by one or by the volume of its cell.…

math.PR2026

Random hyperbolic polyhedra in horoballs

Florian Besau, Anna Gusakova, Christoph Thäle

We study the geodesic convex hull of a stationary Poisson point process restricted to a horoball in $d$ -dimensional hyperbolic space. The resulting random set is an unbounded hyper…

math.PR2026

Limits of Poisson-Laguerre tessellations

Anna Gusakova, Mathias in Wolde-Lübke

For sequences of Poisson-Laguerre tessellations and their duals in $R^{d}$ , generated by Poisson point processes $(η_{n})_{n \in N}$ in $R^{d} \times R$ …

math.PR2025

Critical Poisson hyperplane percolation in hyperbolic space has no unbounded cells

Tillmann Bühler, Anna Gusakova, Konstantin Recke

We show that tessellations of hyperbolic space by isometry-invariant Poisson processes of $(d - 1)$ -dimensional hyperplanes do not have an unbounded cell at the critical intensity. T…

math.PR2025

Gaussian approximation for Extreme Points in Laguerre tessellations

Chinmoy Bhattacharjee, Anna Gusakova

We consider Gaussian approximation in three particular models of Poisson-Laguerre tessellations, namely, the $β$ -, $β^{'}$ - and Gaussian-Voronoi tessellations. The tessellations are c…

math.PR2025

On the moments of the volume for random convex chains

Anna Gusakova, Anna Muranova

Let $T$ be the triangle in the plane with vertices $(0, 0)$ , $(0, 1)$ and $(0, 1)$ . The convex hull $T_{n}$ of points $(0, 1)$ , $(1, 0)$ and $n$ independent random points uniformly di…

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

Percolation of fat Poisson cylinders in hyperbolic space

Carina Betken, Erik Broman, Anna Gusakova +1

In this paper we study Poisson processes of so-called "fat" cylinders in hyperbolic space. As our main result we show that this model undergoes a percolation phase transition. We p…

math.PR2024

Random polytopes in convex bodies: Bridging the gap between extremal containers

Florian Besau, Anna Gusakova, Christoph Thäle

We investigate the asymptotic properties of random polytopes arising as convex hulls of $n$ independent random points sampled from a family of block-beta distributions. Notably, th…

math.PR2024

Concentration inequalities for Poisson $U$ -statistics

Gilles Bonnet, Anna Gusakova

In this article we obtain concentration inequalities for Poisson $U$ -statistics $F_{m} (f, η)$ of order $m \geq 1$ with kernels $f$ under general assumptions on $f$ and the intensity mea…

math.PR2023

Sectional Voronoi tessellations: Characterization and high-dimensional limits

Anna Gusakova, Zakhar Kabluchko, Christoph Thaele

The intersections of beta-Voronoi, beta-prime-Voronoi and Gaussian-Voronoi tessellations in $R^{d}$ with $ℓ$ -dimensional affine subspaces, $1 \leq ℓ \leq d - 1$ , are shown…

math.PR2022

The volume of random simplices from elliptical distributions in high dimension

Anna Gusakova, Johannes Heiny, Christoph Thäle

Random simplices and more general random convex bodies of dimension $p$ in $R^{n}$ with $p \leq n$ are considered, which are generated by random vectors having an elliptical…

math.PR2022

Variance expansion and Berry-Esseen bound for the number of vertices of a random polygon in a polygon

Anna Gusakova, Matthias Reitzner, Christoph Thäle

Fix a container polygon $P$ in the plane and consider the convex hull $P_{n}$ of $n \geq 3$ independent and uniformly distributed in $P$ random points. In the focus of this paper is t…

math.PR2022

Spherical convex hull of random points on a wedge

Florian Besau, Anna Gusakova, Matthias Reitzner +3

Consider two half-spaces $H_{1}^{+}$ and $H_{2}^{+}$ in $R^{d + 1}$ whose bounding hyperplanes $H_{1}$ and $H_{2}$ are orthogonal and pass through the origin. The intersection $\mathbb{…

math.PR2021

The $β$ -Delaunay tessellation IV: Mixing properties and central limit theorems

Anna Gusakova, Zakhar Kabluchko, Christoph Thäle

Various mixing properties of $β$ -, $β^{'}$ - and Gaussian Delaunay tessellations in $R^{d - 1}$ are studied. It is shown that these tessellation models are absolutely regular, o…

math.PR2021

The $β$ -Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions

Anna Gusakova, Zakhar Kabluchko, Christoph Thäle

The $β$ -Delaunay tessellation in $R^{d - 1}$ is a generalization of the classical Poisson-Delaunay tessellation. As a first result of this paper we show that the shape of a…

math.PR2021

The $β$ -Delaunay tessellation II: The Gaussian limit tessellation

Anna Gusakova, Zakhar Kabluchko, Christoph Thäle

We study the weak convergence of $β$ - and $β^{'}$ -Delaunay tessellations in $R^{d - 1}$ that were introduced in part I of this paper, as $β \to \infty$ . The limiting stationary s…

math.PR2020★ 2 cited

On random convex chains, orthogonal polynomials, PF sequences and probabilistic limit theorems

Anna Gusakova, Christoph Thäle

Let $T$ be the triangle in the plane with vertices $(0, 0)$ , $(0, 1)$ and $(0, 1)$ . The convex hull of $(0, 1)$ , $(1, 0)$ and $n$ independent random points uniformly distributed in $T$ …

math.MG2020★ 4 cited

Sharp inequalities for the mean distance of random points in convex bodies

Gilles Bonnet, Anna Gusakova, Christoph Thäle +1

For a convex body $K \subset R^{d}$ the mean distance $Δ (K) = E ∣ X_{1} - X_{2} ∣$ is the expected Euclidean distance of two independent and uniformly distributed random points…

math.PR2020

Concentration on Poisson spaces via modified $Φ$ -Sobolev inequalities

Anna Gusakova, Holger Sambale, Christoph Thaele

Concentration properties of functionals of general Poisson processes are studied. Using a modified $Φ$ -Sobolev inequality a recursion scheme for moments is established, which is of…

math.PR2020★ 1 cited

The $β$ -Delaunay tessellation I: Description of the model and geometry of typical cells

Anna Gusakova, Zakhar Kabluchko, Christoph Thäle

In this paper two new classes of stationary random simplicial tessellations, the so-called $β$ - and $β^{'}$ -Delaunay tessellations, are introduced. Their construction is based on a sp…

math.PR2019★ 1 cited

The volume of simplices in high-dimensional Poisson-Delaunay tessellations

Anna Gusakova, Christoph Thaele

Typical weighted random simplices $Z_{μ}$ , $μ \in (- 2, \infty)$ , in a Poisson-Delaunay tessellation in $R^{n}$ are considered, where the weight is given by the $(μ + 1)$ st power of…

math.PR2019

Concentration inequalities for functionals of Poisson cylinder processes

Anastas Baci, Carina Betken, Anna Gusakova +1

Random union sets $Z$ associated with stationary Poisson processes of $k$ -cylinders in $R^{d}$ are considered. Under general conditions on the typical cylinder base a concen…

Functional central limit theorems for Laguerre tessellations

Random hyperbolic polyhedra in horoballs

Limits of Poisson-Laguerre tessellations

Critical Poisson hyperplane percolation in hyperbolic space has no unbounded cells

Gaussian approximation for Extreme Points in Laguerre tessellations

On the moments of the volume for random convex chains

Sylvester's problem for beta-type distributions

Percolation of fat Poisson cylinders in hyperbolic space

Random polytopes in convex bodies: Bridging the gap between extremal containers

Concentration inequalities for Poisson U-statistics

Sectional Voronoi tessellations: Characterization and high-dimensional limits

The volume of random simplices from elliptical distributions in high dimension

Variance expansion and Berry-Esseen bound for the number of vertices of a random polygon in a polygon

Spherical convex hull of random points on a wedge

The β-Delaunay tessellation IV: Mixing properties and central limit theorems

The β-Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions

The β-Delaunay tessellation II: The Gaussian limit tessellation

On random convex chains, orthogonal polynomials, PF sequences and probabilistic limit theorems

Sharp inequalities for the mean distance of random points in convex bodies

Concentration on Poisson spaces via modified Φ-Sobolev inequalities

The β-Delaunay tessellation I: Description of the model and geometry of typical cells

The volume of simplices in high-dimensional Poisson-Delaunay tessellations

Concentration inequalities for functionals of Poisson cylinder processes

Concentration inequalities for Poisson $U$ -statistics

The $β$ -Delaunay tessellation IV: Mixing properties and central limit theorems

The $β$ -Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions

The $β$ -Delaunay tessellation II: The Gaussian limit tessellation

Concentration on Poisson spaces via modified $Φ$ -Sobolev inequalities

The $β$ -Delaunay tessellation I: Description of the model and geometry of typical cells