On random disc-polygons in a disc-polygon
Ferenc Fodor, P\'eter Kevei, Viktor V\'igh

TL;DR
This paper derives asymptotic formulas for the expected number of vertices and missed area of random disc-polygons within convex disc-polygons, extending classical convex polygon results to the $r$-convex setting.
Contribution
It introduces $r$-convex analogues of classical results, providing new asymptotic formulas for random disc-polygons in convex disc-polygons.
Findings
Derived asymptotic formulas for vertex number and missed area
Extended classical convex polygon results to $r$-convex case
Provides theoretical foundation for random disc-polygons analysis
Abstract
We prove asymptotic formulas for the expectation of the vertex number and missed area of uniform random disc-polygons in convex disc-polygons. Our statements are the -convex analogues of the classical results of R\'enyi and Sulanke (1964) about random polygons in convex polygons.
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