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On Random Disc Polygons in Smooth Convex Discs

Part of: Geometric probability and stochastic geometry General convexity

Published online by Cambridge University Press:  22 February 2016

F. Fodor ,
P. Kevei  and
V. Vígh
F. Fodor*
Affiliation:
University of Szeged and University of Calgary
P. Kevei*
Affiliation:
MTA-SZTE Analysis and Stochastics Research Group
V. Vígh*
Affiliation:
University of Szeged
*
∗ Postal address: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary.
∗ Postal address: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary.
∗ Postal address: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary.
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Abstract

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In this paper we generalize some of the classical results of Rényi and Sulanke (1963), (1964) in the context of spindle convexity. A planar convex disc S is spindle convex if it is the intersection of congruent closed circular discs. The intersection of finitely many congruent closed circular discs is called a disc polygon. We prove asymptotic formulae for the expectation of the number of vertices, missed area, and perimeter difference of uniform random disc polygons contained in a sufficiently smooth spindle convex disc.

Keywords

Convex discdisc polygonspindle convexityrandom approximation

MSC classification

Primary: 52A22: Random convex sets and integral geometry
Secondary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 46 , Issue 4 , December 2014 , pp. 899 - 918
Copyright
© Applied Probability Trust 

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