Asymptotic normality for random simplices and convex bodies in high dimensions
| Autor: | Julian Grote, Elisabeth M. Werner, Zakhar Kabluchko, Christoph Thäle, Florian Besau, David Alonso-Gutiérrez, Matthias Reitzner, Beatrice-Helen Vritsiou |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Independent and identically distributed random variables
Applied Mathematics General Mathematics 010102 general mathematics Probability (math.PR) Regular polygon Asymptotic distribution Metric Geometry (math.MG) 16. Peace & justice 01 natural sciences Combinatorics 010104 statistics & probability Cone (topology) Mathematics - Metric Geometry 52A22 52A23 60D05 60F05 FOS: Mathematics Ball (mathematics) 0101 mathematics Stochastic geometry Mathematics - Probability Central limit theorem Mathematics Probability measure |
| Zdroj: | Zaguán: Repositorio Digital de la Universidad de Zaragoza Universidad de Zaragoza Zaguán. Repositorio Digital de la Universidad de Zaragoza instname |
| Popis: | Central limit theorems for the log-volume of a class of random convex bodies in R n \mathbb {R}^n are obtained in the high-dimensional regime, that is, as n → ∞ 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 n -dimensional ℓ p \ell _p -ball. In particular, this includes the cone and the uniform probability measure. |
| Databáze: | OpenAIRE |
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