The Annals of Probability
- Ann. Probab.
- Volume 39, Number 3 (2011), 881-903.
Central limit theorems for random polygons in an arbitrary convex set
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.
Ann. Probab., Volume 39, Number 3 (2011), 881-903.
First available in Project Euclid: 16 March 2011
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 52A22: Random convex sets and integral geometry [See also 53C65, 60D05] 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60F05: Central limit and other weak theorems
Pardon, John. Central limit theorems for random polygons in an arbitrary convex set. Ann. Probab. 39 (2011), no. 3, 881--903. doi:10.1214/10-AOP568. https://projecteuclid.org/euclid.aop/1300281727