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1 results

  • On Random Disc Polygons in Smooth Convex Discs

  • Part of
  • F. Fodor, P. Kevei, V. Vígh
  • Journal:
    Advances in Applied Probability / Volume 46 / Issue 4 / December 2014
    Published online by Cambridge University Press:
    22 February 2016, pp. 899-918
    Print publication:
    December 2014
    • Article
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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.