Zobrazeno 1 - 10
of 29
pro vyhledávání: '"Grote, Julian"'
Autor:
Alonso-Gutiérrez, David, Besau, Florian, Grote, Julian, Kabluchko, Zakhar, Reitzner, Matthias, Thäle, Christoph, Vritsiou, Beatrice-Helen, Werner, Elisabeth M.
Central limit theorems for the log-volume of a class of random convex bodies in $\mathbb{R}^n$ are obtained in the high-dimensional regime, that is, as $n\to\infty$. In particular, the case of random simplices pinned at the origin and simplices where
Externí odkaz:
http://arxiv.org/abs/1906.02471
The deviation of a general convex body with twice differentiable boundary and an arbitrarily positioned polytope with a given number of vertices is studied. The paper considers the case where the deviation is measured in terms of the surface areas of
Externí odkaz:
http://arxiv.org/abs/1811.04656
Autor:
Grote, Julian
Fix a space dimension $d\ge 2$, parameters $\alpha > -1$ and $\beta \ge 1$, and let $\gamma_{d,\alpha, \beta}$ be the probability measure of an isotropic random vector in $\mathbb{R}^d$ with density proportional to \begin{align*} ||x||^\alpha\, \exp\
Externí odkaz:
http://arxiv.org/abs/1808.09779
Let $X_1,\ldots,X_N$, $N>n$, be independent random points in $\mathbb{R}^n$, distributed according to the so-called beta or beta-prime distribution, respectively. We establish threshold phenomena for the volume, intrinsic volumes, or more general mea
Externí odkaz:
http://arxiv.org/abs/1802.04089
Let $r=r(n)$ be a sequence of integers such that $r\leq n$ and let $X_1,\ldots,X_{r+1}$ be independent random points distributed according to the Gaussian, the Beta or the spherical distribution on $\mathbb{R}^n$. Limit theorems for the log-volume an
Externí odkaz:
http://arxiv.org/abs/1708.00471
Autor:
Grote, Julian, Werner, Elisabeth M.
Let $K$ be a convex body in $\mathbb{R}^n$ and $f : \partial K \rightarrow \mathbb{R}_+$ a continuous, strictly positive function with $\int\limits_{\partial K} f(x) d \mu_{\partial K}(x) = 1$. We give an upper bound for the approximation of $K$ in t
Externí odkaz:
http://arxiv.org/abs/1706.07623
Autor:
Bonnet, Gilles, Grote, Julian, Temesvari, Daniel, Thaele, Christoph, Turchi, Nicola, Wespi, Florian
Publikováno v:
Journal of Mathematical Analysis and Applications 455, 1351-1364 (2017)
Let $X_1,\ldots,X_n$ be independent random points that are distributed according to a probability measure on $\mathbb{R}^d$ and let $P_n$ be the random convex hull generated by $X_1,\ldots,X_n$ ($n\geq d+1$). Natural classes of probability distributi
Externí odkaz:
http://arxiv.org/abs/1703.02321
Autor:
Grote, Julian, Thaele, Christoph
The random convex hull of a Poisson point process in $\mathbb{R}^d$ whose intensity measure is a multiple of the standard Gaussian measure on $\mathbb{R}^d$ is investigated. The purpose of this paper is to invent a new viewpoint on these Gaussian pol
Externí odkaz:
http://arxiv.org/abs/1602.06148
Publikováno v:
In Advances in Applied Mathematics August 2021 129
Autor:
Grote, Julian, Thaele, Christoph
The convex hull generated by the restriction to the unit ball of a stationary Poisson point process in the $d$-dimensional Euclidean space is considered. By establishing sharp bounds on cumulants, exponential estimates for large deviation probabiliti
Externí odkaz:
http://arxiv.org/abs/1508.04994