A. Gusakova

activity

20242026

collaborators

8 papers

math.PR2026

Limits of Poisson-Laguerre tessellations

Anna Gusakova, Mathias in Wolde-LÃ¼bke

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

math.PR2025

Critical Poisson hyperplane percolation in hyperbolic space has no unbounded cells

Tillmann BÃ¼hler, 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 $I^^{2}$ -, $Î²'$- and Gaussian-Voronoi tessellations. The tessellations are…

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…