Abstract
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.
Citation
John Pardon. "Central limit theorems for random polygons in an arbitrary convex set." Ann. Probab. 39 (3) 881 - 903, May 2011. https://doi.org/10.1214/10-AOP568
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