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Variance estimates for random disc-polygons in smooth convex discs

Part of: General convexity Geometric probability and stochastic geometry

Published online by Cambridge University Press:  16 January 2019

Ferenc Fodor  and
Viktor Vígh
Ferenc Fodor*
Affiliation:
University of Szeged
Viktor Vígh*
Affiliation:
University of Szeged
*
* Postal address: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary.
* Postal address: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary.
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Abstract

In this paper we prove asymptotic upper bounds on the variance of the number of vertices and the missed area of inscribed random disc-polygons in smooth convex discs whose boundary is C+2. We also consider a circumscribed variant of this probability model in which the convex disc is approximated by the intersection of random circles.

Keywords

Disc-polygonrandom approximationvariance

MSC classification

Primary: 52A22: Random convex sets and integral geometry
Secondary: 60D05: Geometric probability and stochastic geometry
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 4 , December 2018 , pp. 1143 - 1157
Copyright
Copyright © Applied Probability Trust 2018 

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