Asymptotic normality for random simplices and convex bodies in high dimensions

Alonso Gutiérrez, David (Universidad de Zaragoza) ; Besau, Florian ; Grote, Julian ; Kabluchko, Zakhar ; Reitzner, Matthias ; Thäle, Christoph ; Vritsiou Beatrice-Helen ; Werner, Elizabeth

Resumen: 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.

Idioma: Inglés

DOI: 10.1090/proc/15232

Año: 2021

Publicado en: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 149 (2021), 355-367
ISSN: 0002-9939

Factor impacto JCR: 0.971 (2021)

Categ. JCR: MATHEMATICS rank: 166 / 333 = 0.498 (2021) - Q2 - T2
Categ. JCR: MATHEMATICS, APPLIED rank: 207 / 267 = 0.775 (2021) - Q4 - T3

Factor impacto CITESCORE: 1.7 - Mathematics (Q3)

Factor impacto SCIMAGO: 0.891 - Mathematics (miscellaneous) (Q1) - Applied Mathematics (Q1)

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)