A. Gusakova

activity

20192022

collaborators

5 papers

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 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.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…