A central limit theorem for random disc-polygons in smooth convex discs

A central limit theorem for random disc-polygons in smooth convex discs

In this paper we prove a quantitative central limit theorem for the area of uniform random disc-polygons in smooth convex discs whose boundary is \(C^2_+\). We use Stein's method and the asymptotic lower bound for the variance of the area proved by Fodor, Gr\"unfelder and Vígh (2022).

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Veröffentlicht in:arXiv.org 2023-10
Hauptverfasser: Fodor, Ferenc, Papvári, Dániel I
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic methods
Lower bounds
Polygons
Theorems
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Zusammenfassung:In this paper we prove a quantitative central limit theorem for the area of uniform random disc-polygons in smooth convex discs whose boundary is \(C^2_+\). We use Stein's method and the asymptotic lower bound for the variance of the area proved by Fodor, Gr\"unfelder and Vígh (2022).
ISSN:2331-8422