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 $C_{+}^2$. We use Stein's method and the asymptotic lower bound for the variance of the area proved by Fodor, Grünfelder and Vígh (2022).

References in corpus (5)

• A new method of normal approximation
• Poisson polytopes
• Ball and Spindle Convexity with respect to a Convex Body
• Variance estimates for random disc-polygons in smooth convex discs
• Variance bounds for disc-polygons