Advances in Applied Probability

On random disc polygons in smooth convex discs

F. Fodor, P. Kevei, and V. Vígh

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Abstract

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.

Article information

Source
Adv. in Appl. Probab., Volume 46, Number 4 (2014), 899-918.

Dates
First available in Project Euclid: 12 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.aap/1418396236

Digital Object Identifier
doi:10.1239/aap/1418396236

Mathematical Reviews number (MathSciNet)
MR3290422

Zentralblatt MATH identifier
1314.52004

Subjects
Primary: 52A22: Random convex sets and integral geometry [See also 53C65, 60D05]
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Keywords
Convex disc disc polygon spindle convexity random approximation

Citation

Fodor, F.; Kevei, P.; Vígh, V. On random disc polygons in smooth convex discs. Adv. in Appl. Probab. 46 (2014), no. 4, 899--918. doi:10.1239/aap/1418396236. https://projecteuclid.org/euclid.aap/1418396236


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