ASYMPTOTIC NORMALITY FOR RANDOM SIMPLICES AND CONVEX BODIES IN HIGH DIMENSIONS
Autor(en): | Alonso-Gutierrez, D. Besau, F. Grote, J. Kabluchko, Z. Reitzner, M. Thale, C. Vritsiou, B-H Werner, E. |
Stichwörter: | BALL; Central limit theorem; high dimensions; l(p)-ball; Mathematics; Mathematics, Applied; random convex body; random determinant; random parallelotope; random polytope; random simplex; stochastic geometry; VOLUME | Erscheinungsdatum: | 2021 | Herausgeber: | AMER MATHEMATICAL SOC | Journal: | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | Volumen: | 149 | Ausgabe: | 1 | Startseite: | 355 | Seitenende: | 367 | Zusammenfassung: | Central limit theorems for the log-volume of a class of random convex bodies in R-n are obtained in the high-dimensional regime, that is, as n -> infinity. 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 (s)ymmetric probability measure on the n-dimensional l(p)-ball. In particular, this includes the cone and the uniform probability measure. |
ISSN: | 00029939 | DOI: | 10.1090/proc/15232 |
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geprüft am 12.05.2024