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

Abstract 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 $$C^2_+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> . 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).