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May 2011 Central limit theorems for random polygons in an arbitrary convex set
John Pardon
Ann. Probab. 39(3): 881-903 (May 2011). DOI: 10.1214/10-AOP568


We study the probability distribution of the area and the number of vertices of random polygons in a convex set K⊂ℝ2. The novel aspect of our approach is that it yields uniform estimates for all convex sets K⊂ℝ2 without imposing any regularity conditions on the boundary ∂K. Our main result is a central limit theorem for both the area and the number of vertices, settling a well-known conjecture in the field. We also obtain asymptotic results relating the growth of the expectation and variance of these two functionals.


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John Pardon. "Central limit theorems for random polygons in an arbitrary convex set." Ann. Probab. 39 (3) 881 - 903, May 2011.


Published: May 2011
First available in Project Euclid: 16 March 2011

zbMATH: 1221.52011
MathSciNet: MR2789578
Digital Object Identifier: 10.1214/10-AOP568

Primary: 52A22 , 60D05 , 60F05

Keywords: central limit theorem , Random polygons

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 3 • May 2011
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