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pro vyhledávání: '"A Thäle"'
Consider a stationary Poisson process $\eta$ in a $d$-dimensional hyperbolic space of constant curvature $-\varkappa$ and let the points of $\eta$ together with a fixed origin $o$ be the vertices of a graph. Connect each point $x\in\eta$ with its rad
Externí odkaz:
http://arxiv.org/abs/2408.15131
Consider the $d$-dimensional hyperbolic space $\mathbb{M}_K^d$ of constant curvature $K<0$ and fix a point $o$ playing the role of an origin. Let $\mathbf{L}$ be a uniform random $q$-dimensional totally geodesic submanifold (called $q$-flat) in $\mat
Externí odkaz:
http://arxiv.org/abs/2407.10708
Consider a uniformly distributed random linear subspace $L$ and a stochastically independent random affine subspace $E$ in $\mathbb{R}^n$, both of fixed dimension. For a natural class of distributions for $E$ we show that the intersection $L\cap E$ a
Externí odkaz:
http://arxiv.org/abs/2404.14253
The purpose of this paper is to introduce the new concept of weighted floating functions associated with log concave or $s$-concave functions. This leads to new notions of weighted functional affine surface areas. Their relation to more traditional v
Externí odkaz:
http://arxiv.org/abs/2403.02925
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 different weights. Such a random polygon can only be a triangle, a quadrila
Externí odkaz:
http://arxiv.org/abs/2309.12771
Autor:
Sonnleitner, Mathias, Thäle, Christoph
The purpose of this note is to study the asymptotic volume of intersections of unit balls associated with two norms in $\mathbb{R}^n$ as their dimension $n$ tends to infinity. A general framework is provided and then specialized to the following case
Externí odkaz:
http://arxiv.org/abs/2308.10635
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 process of unit intensity in a growing sampling window in hyperbolic sp
Externí odkaz:
http://arxiv.org/abs/2304.08744
Autor:
Schulte, Matthias, Thaele, Christoph
This paper deals with U-statistics of Poisson processes and multiple Wiener-It\^o integrals on the Poisson space. Via sharp bounds on the cumulants for both classes of random variables, moderate deviation principles, concentration inequalities and no
Externí odkaz:
http://arxiv.org/abs/2304.00876
Consider a stationary Poisson process of horospheres in a $d$-dimensional hyperbolic space. In the focus of this note is the total surface area these random horospheres induce in a sequence of balls of growing radius $R$. The main result is a quantit
Externí odkaz:
http://arxiv.org/abs/2303.17827
Poisson processes in the space of $k$-dimensional totally geodesic subspaces ($k$-flats) in a $d$-dimensional standard space of constant curvature $\kappa\in\{-1,0,1\}$ are studied, whose distributions are invariant under the isometries of the space.
Externí odkaz:
http://arxiv.org/abs/2302.09524