A Central Limit Theorem for Random Disc-Polygons in Smooth Convex Discs

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2024年11月18日

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Ferenc Fodor,
Dániel I. Papvári

摘要

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).