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- W2890599768 abstract "We study the concentration of the norm of a random vector $Y$ uniformly sampled in the centered zero cell of two types of stationary and isotropic random mosaics in $mathbb{R}^n$ for large dimensions $n$. For a stationary and isotropic Poisson-Voronoi mosaic, $Y$ has a radial and log-concave distribution, implying that ${|Y|}/{mathbb{E}(|Y|^2)^{frac{1}{2}}}$ approaches one for large $n$. Assuming the cell intensity of the random mosaic scales like $e^{n rho_n}$, where $lim_{n to infty} rho_n = rho$, $|Y|$ is on the order of $sqrt{n}$ for large $n$. For the Poisson-Voronoi mosaic, we show that $|Y|/sqrt{n}$ concentrates to $e^{-rho}(2pi e)^{-frac{1}{2}}$ as $n$ increases, and for a stationary and isotropic Poisson hyperplane mosaic, we show there is a range $(R_{ell}, R_u)$ such that ${|Y|}/{sqrt{n}}$ will be within this range with high probability for large $n$. The rates of convergence are also computed in both cases." @default.
- W2890599768 created "2018-09-27" @default.
- W2890599768 creator A5022642787 @default.
- W2890599768 date "2018-09-11" @default.
- W2890599768 modified "2023-09-27" @default.
- W2890599768 title "Thin-shell concentration for zero cells of stationary Poisson mosaics." @default.
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