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 $$C^2_+$$ C + 2 . We use Stein’s method and the asymptotic lower bound for the variance of the area proved by Fodor, Grünfelder and Vígh (Doc Math 27: 101...

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Veröffentlicht in:Discrete & computational geometry 2024-11
Hauptverfasser: Fodor, Ferenc, Papvári, Dániel I.
Format: Artikel
Sprache:eng
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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 $$C^2_+$$ C + 2 . We use Stein’s method and the asymptotic lower bound for the variance of the area proved by Fodor, Grünfelder and Vígh (Doc Math 27: 1015-1029, 2022).
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-024-00701-6