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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>2_+$$\end{document}. We use Stein's method and the asymptotic lower bound for the variance of the area proved by Fodor, Gr & uuml;nfelder and V & iacute;gh (Doc Math 27: 1015-1029, 2022).