CENTRAL LIMIT THEOREMS FOR RANDOM POLYGONS IN AN ARBITRARY CONVEX SET
成果类型：
Article
署名作者：
Pardon, John
署名单位：
Princeton University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/10-AOP568
发表日期：
2011
页码：
881-903
关键词：
摘要：
We study the probability distribution of the area and the number of vertices of random polygons in a convex set K subset of R-2. The novel aspect of our approach is that it yields uniform estimates for all convex sets K subset of R-2 without imposing any regularity conditions on the boundary partial derivative K. Our main result is a central limit theorem for both the area and the number of vertices, setting a well-known conjecture in the field. We also obtain asymptotic results relating the growth of the expectation and variance of these two functionals.