Variance bounds for disc-polygons

Variance bounds for disc-polygons

We prove asymptotic lower bounds on the variance of the number of vertices and missed area of random disc-polygons in convex discs whose boundary is \(C_+^2\) smooth. The established lower bounds are of the same order as the upper bounds proved previously by Fodor and V\'ıgh (2018).

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Veröffentlicht in:arXiv.org 2021-11
Hauptverfasser: Fodor, Ferenc, Grünfelder, Balázs, Vígh, Viktor
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Lower bounds
Polygons
Upper bounds
Variance
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Zusammenfassung:We prove asymptotic lower bounds on the variance of the number of vertices and missed area of random disc-polygons in convex discs whose boundary is \(C_+^2\) smooth. The established lower bounds are of the same order as the upper bounds proved previously by Fodor and V\'ıgh (2018).
ISSN:2331-8422