15 citations · 101 across the 48 of their papers we have counts for
53 papers · 1 filter
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 -dimensional hyperbolic space. The resulting random set is an unbounded hyper…
Lengths and incidences in Poisson hypersphere and spherical splitting tessellations
Daniel Hug, Christoph Thäle
We investigate distributional properties of two random tessellation models on the -dimen\-sional unit sphere. First, we analyze the Poisson hypersphere tessellation generated by…
Realising atomless laws as distance distributions on metric measure spaces
Christoph Thäle, Philipp Tuchel
We study which probability measures on can occur as the distribution of the distance between two independent points sampled from a complete separable metric space equi…
Mod-phi convergence for random variables with cyclotomic generating functions
Christoph Thäle, Philipp Tuchel
We consider a sequence of discrete random variables whose generating functions are polynomials only having roots on the unit circle in the complex plane. For such sequences we prov…
Intersection probabilities for flats in hyperbolic space
Ercan Sönmez, Panagiotis Spanos, Christoph Thäle
Consider the -dimensional hyperbolic space of constant curvature and fix a point playing the role of an origin. Let be a uniform random $…
Quantification of the Fourth Moment Theorem for Cyclotomic Generating Functions
Benedikt Rednoß, Christoph Thäle
This paper deals with sequences of random variables only taking values in . The probability generating functions of such random variables are polynomials of d…
Vertex number of the typical cell in a tri-directional Poisson line tessellation
Nils Heerten, Janina Hübner, Christoph Thäle
This paper deals with the typical cell in a Poisson line tessellation in the plane whose directional distribution is concentrated on three equally spread values with possibly diffe…
Moderate deviations on Poisson chaos
Matthias Schulte, Christoph Thaele
This paper deals with U-statistics of Poisson processes and multiple Wiener-Itô integrals on the Poisson space. Via sharp bounds on the cumulants for both classes of random variabl…
A quantitative central limit theorem for Poisson horospheres in high dimensions
Zakhar Kabluchko, Daniel Rosen, Christoph Thäle
Consider a stationary Poisson process of horospheres in a -dimensional hyperbolic space. In the focus of this note is the total surface area these random horospheres induce in a…
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 with -dimensional affine subspaces, , are shown…
Large nearest neighbour balls in hyperbolic stochastic geometry
Moritz Otto, Christoph Thaele
Consider a stationary Poisson process in a -dimensional hyperbolic space. For define the point process of exceedance heights over a suitable threshold of the h…
Probabilistic Limit Theorems Induced by the Zeros of Polynomials
Nils Heerten, Holger Sambale, Christoph Thäle
Sequences of discrete random variables are studied whose probability generating functions are zero-free in a sector of the complex plane around the positive real axis. Sharp bounds…
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 in with are considered, which are generated by random vectors having an elliptical…
Fluctuations of -geodesic Poisson hyperplanes in hyperbolic space
Zakhar Kabluchko, Daniel Rosen, Christoph Thäle
Poisson processes of so-called -geodesic hyperplanes in -dimensional hyperbolic space are studied for . The case corresponds to genuine geodesic hyperplan…
Weighted -radial Distributions on Euclidean and Matrix -balls with Applications to Large Deviations
Tom Kaufmann, Christoph Thaele
A probabilistic representation for a class of weighted -radial distributions, based on mixtures of a weighted cone probability measure and a weighted uniform distribution on the…
Beta-star polytopes and hyperbolic stochastic geometry
Thomas Godland, Zakhar Kabluchko, Christoph Thäle
Motivated by problems of hyperbolic stochastic geometry we introduce and study the class of beta-star polytopes. A beta-star polytope is defined as the convex hull of an inhomogene…
A simplified second-order Gaussian Poincaré inequality in discrete setting with applications
Peter Eichelsbacher, Benedikt Rednoß, Christoph Thäle +1
In this paper, a simplified second-order Gaussian Poincaré inequality for normal approximation of functionals over infinitely many Rademacher random variables is derived. It is bas…
The -Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions
Anna Gusakova, Zakhar Kabluchko, Christoph Thäle
The -Delaunay tessellation in is a generalization of the classical Poisson-Delaunay tessellation. As a first result of this paper we show that the shape of a…
Random cones in high dimensions I: Donoho-Tanner and Cover-Efron cones
Thomas Godland, Zakhar Kabluchko, Christoph Thaele
Two models of random cones in high dimensions are considered, together with their duals. The Donoho-Tanner random cone can be defined as the positive hull of independ…
On random convex chains, orthogonal polynomials, PF sequences and probabilistic limit theorems
Anna Gusakova, Christoph Thäle
Let be the triangle in the plane with vertices , and . The convex hull of , and independent random points uniformly distributed in …
Concentration on Poisson spaces via modified -Sobolev inequalities
Anna Gusakova, Holger Sambale, Christoph Thaele
Concentration properties of functionals of general Poisson processes are studied. Using a modified -Sobolev inequality a recursion scheme for moments is established, which is of…
The -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 - and -Delaunay tessellations, are introduced. Their construction is based on a sp…
A new approach to weak convergence of random cones and polytopes
Zakhar Kabluchko, Daniel Temesvari, Christoph Thäle
A new approach to prove weak convergence of random polytopes on the space of compact convex sets is presented. This is used to show that the profile of the rescaled Schläfli random…
Multi-Dimensional Normal Approximation of Heavy-Tailed Moving Averages
Ehsan Azmoodeh, Mathias Mørck Ljungdahl, Christoph Thäle
In this paper we extend the refined second-order Poincaré inequality for Poisson functionals from a one-dimensional to a multi-dimensional setting. Its proof is based on a multivar…