doi:10.1090/proc/15232engAlonso Gutiérrez, DavidBesau, FlorianGrote, JulianKabluchko, ZakharReitzner, MatthiasThäle, ChristophVritsiou Beatrice-HelenWerner, ElizabethAsymptotic normality for random simplices and convex bodies in high dimensionsART-2021-120359Central 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.2021http://zaguan.unizar.es/record/9575810.1090/proc/15232http://zaguan.unizar.es/record/95758oai:zaguan.unizar.es:95758PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 149 (2021), 355-367by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess