Christoph Thale

activity

20142026

most citedFunctional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry

40 citations · 48 across the 27 of their papers we have counts for

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27 papers · 1 filter

math.PR2026

Face volume densities of positive-intensity and ideal Poisson--Voronoi tessellations in hyperbolic spaces

Matteo D'Achille, Christoph Thäle

We determine analytically for all $k \in {0, 1, \dots, d - 1}$ the $k$ -volume densities of a Poisson--Voronoi tessellation of intensity $λ > 0$ in the $d$ -dimensional hyperbolic space of…

math.PR2026

Visibility in the Boolean Model on Harmonic Manifolds

Enkelejd Hashorva, Christoph Thäle

In Poisson Boolean models with deterministic ball grains, the directional visible range from an uncovered point is known to be exponentially distributed in Euclidean and real hyper…

math.PR2026

Central Limit Theorem for Random Partial Sphere Coverings in High Dimensions

Steven Hoehner, Christoph Thäle

We study a random partial covering model on the $(d - 1)$ -dimensional unit sphere, where $N$ spherical caps are placed independently and uniformly at random, each covering a surface…

math.PR2026

The volume of hyperbolic Poisson zero cells: critical divergence and exact second moment

Tillmann Bühler, Christoph Thäle

We investigate the second volume moment of the zero cell $Z_{o}$ of a Poisson hyperplane tessellation with intensity $γ$ in the $d$ -dimensional hyperbolic space. We focus on the phas…

math.PR2025

Random convex chains through the lens of analytic combinatorics

Florian Besau, Christoph Thäle

Consider the triangle $T$ with vertices $(0, 0)$ , $(0, 1)$ , and $(1, 0)$ . The lower boundary of the convex hull of $(0, 1)$ , $(1, 0)$ , together with $n$ independent uniformly distribute…

math.PR2025

Wicksell's corpuscle problem in spaces of constant curvature

Panagiotis Spanos, Christoph Thäle

In this paper, we study Wicksell's corpuscle problem in spaces of constant curvature, thus extending the classical Euclidean framework. We consider a particle process of balls with…

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★ 1 cited

The radial spanning tree in hyperbolic space

Daniel Rosen, Matthias Schulte, Christoph Thäle +1

Consider a stationary Poisson process $η$ in a $d$ -dimensional hyperbolic space of constant curvature $- ϰ$ and let the points of $η$ together with a fixed origin $o$ be the…

math.PR2023

A note on critical intersections of classical and Schatten $p$ -balls

Mathias Sonnleitner, Christoph Thäle

The purpose of this note is to study the asymptotic volume of intersections of unit balls associated with two norms in $R^{n}$ as their dimension $n$ tends to infinity. A ge…

math.PR2023★ 1 cited

Large deviations for hyperbolic $k$ -nearest neighbor balls

Christian Hirsch, Moritz Otto, Takashi Owada +1

We prove a large deviation principle for the point process of large Poisson $k$ -nearest neighbor balls in hyperbolic space. More precisely, we consider a stationary Poisson point p…

math.PR2023

Intersections of Poisson $k$ -flats in constant curvature spaces

Carina Betken, Daniel Hug, Christoph Thäle

Poisson processes in the space of $k$ -dimensional totally geodesic subspaces ( $k$ -flats) in a $d$ -dimensional standard space of constant curvature $κ \in {- 1, 0, 1}$ are studied, who…

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

Large deviations for uniform projections of $p$ -radial distributions on $ℓ_{p}^{n}$ -balls

Tom Kaufmann, Holger Sambale, Christoph Thäle

We consider products of uniform random variables from the Stiefel manifold of orthonormal $k$ -frames in $R^{n}$ , $k \leq n$ , and random vectors from the $n$ -dimensional $\ell…

math.PR2022

Asymptotic expected $T$ -functionals of random polytopes with applications to $L_{p}$ surface areas

Steven Hoehner, Ben Li, Michael Roysdon +1

An asymptotic formula is proved for the expected $T$ -functional of the convex hull of independent and identically distributed random points sampled from the Euclidean unit sphere i…

math.PR2021

Sharpening the probabilistic Arithmetic-Geometric Mean Inequality

Tom Kaufmann, Christoph Thäle

We consider the $p$ -generalized arithmetic-geometric mean inequality for vectors chosen randomly from the $ℓ_{p}^{n}$ -ball in $R^{n}$ . In this setting the inequality can be i…

math.PR2021

Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes

Carina Betken, Matthias Schulte, Christoph Thäle

This paper deals with the union set of a stationary Poisson process of cylinders in $R^{n}$ having an $(n - m)$ -dimensional base and an $m$ -dimensional direction space, where…

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

Optimal Variance--Gamma approximation on the second Wiener chaos

Ehsan Azmoodeh, Peter Eichelsbacher, Christoph Thäle

In this paper, we consider a target random variable $Y \sim \CVG$ distributed according to a centered Variance--Gamma distribution. For a generic random element $F = I_{2} (f)$ in the s…

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

Weak convergence of the intersection point process of Poisson hyperplanes

Anastas Baci, Gilles Bonnet, Christoph Thäle

This paper deals with the intersection point process of a stationary and isotropic Poisson hyperplane process in $R^{d}$ of intensity $t > 0$ , where only hyperplanes that inte…

math.PR2020

Faces in random great hypersphere tessellations

Zakhar Kabluchko, Christoph Thäle

The concept of typical and weighted typical spherical faces for tessellations of the $d$ -dimensional unit sphere, generated by $n$ independent random great hyperspheres distributed…

math.PR2019

Asymptotic normality for random polytopes in non-Euclidean geometries

Florian Besau, Christoph Thäle

Asymptotic normality for the natural volume measure of random polytopes generated by random points distributed uniformly in a convex body in spherical or hyperbolic spaces is prove…

math.PR2019★ 2 cited

A Berry-Esseén theorem for partial sums of functionals of heavy-tailed moving averages

Andreas Basse-O'Connor, Mark Podolskij, Christoph Thäle

In this paper we obtain Berry-Esseén bounds on partial sums of functionals of heavy-tailed moving averages, including the linear fractional stable noise, stable fractional ARIMA pr…

Face volume densities of positive-intensity and ideal Poisson--Voronoi tessellations in hyperbolic spaces

Visibility in the Boolean Model on Harmonic Manifolds

Central Limit Theorem for Random Partial Sphere Coverings in High Dimensions

The volume of hyperbolic Poisson zero cells: critical divergence and exact second moment

Random convex chains through the lens of analytic combinatorics

Wicksell's corpuscle problem in spaces of constant curvature

Percolation of fat Poisson cylinders in hyperbolic space

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

The radial spanning tree in hyperbolic space

A note on critical intersections of classical and Schatten p-balls

Large deviations for hyperbolic k-nearest neighbor balls

Intersections of Poisson k-flats in constant curvature spaces

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

Large deviations for uniform projections of p-radial distributions on ℓpn​-balls

Asymptotic expected T-functionals of random polytopes with applications to Lp​ surface areas

Sharpening the probabilistic Arithmetic-Geometric Mean Inequality

Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes

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

Optimal Variance--Gamma approximation on the second Wiener chaos

The β-Delaunay tessellation II: The Gaussian limit tessellation

Weak convergence of the intersection point process of Poisson hyperplanes

Faces in random great hypersphere tessellations

Asymptotic normality for random polytopes in non-Euclidean geometries

A Berry-Esseén theorem for partial sums of functionals of heavy-tailed moving averages

A note on critical intersections of classical and Schatten $p$ -balls

Large deviations for hyperbolic $k$ -nearest neighbor balls

Intersections of Poisson $k$ -flats in constant curvature spaces

Large deviations for uniform projections of $p$ -radial distributions on $ℓ_{p}^{n}$ -balls

Asymptotic expected $T$ -functionals of random polytopes with applications to $L_{p}$ surface areas

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

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