95758 20230519145354.0 doi 10.1090/proc/15232 sideral 120359 ART-2021-120359 eng Alonso Gutiérrez, David Universidad de Zaragoza (orcid)0000-0003-1256-3671 Asymptotic normality for random simplices and convex bodies in high dimensions 2021 Access copy available to the general public Unrestricted 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 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 also established 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. info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 0.971 2021 MATHEMATICS 166 / 333 = 0.498 2021 Q2 T2 MATHEMATICS, APPLIED 207 / 267 = 0.775 2021 Q4 T3 0.891 2021 Mathematics (miscellaneous) 2021 Q1 Applied Mathematics 2021 Q1 1.7 2021 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Besau, Florian Grote, Julian Kabluchko, Zakhar Reitzner, Matthias Thäle, Christoph Vritsiou Beatrice-Helen Werner, Elizabeth 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 149 (2021), 355-367 Proc. Am. Math. Soc. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 0002-9939 464082 http://zaguan.unizar.es/record/95758/files/texto_completo.pdf Postprint 334359 http://zaguan.unizar.es/record/95758/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:95758 articulos driver 2023-05-18-13:29:54 ARTICLE