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- W4288334927 abstract "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 $ntoinfty$. In particular, the case of random simplices pinned at the origin and simplices where all vertices are generated at random is investigated. The coordinates of the generating vectors are assumed to be independent and identically distributed with subexponential tails. In addition, asymptotic normality is established also for random convex bodies (including random simplices pinned at the origin) when the spanning vectors are distributed according to a radially symmetric probability measure on the $n$-dimensional $ell_p$-ball. In particular, this includes the cone and the uniform probability measure." @default.
- W4288334927 created "2022-07-28" @default.
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- W4288334927 date "2019-06-06" @default.
- W4288334927 modified "2023-10-17" @default.
- W4288334927 title "Asymptotic normality for random simplices and convex bodies in high dimensions" @default.
- W4288334927 doi "https://doi.org/10.48550/arxiv.1906.02471" @default.
- W4288334927 hasPublicationYear "2019" @default.
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