On asymptotic properties of the perimeter of a convex hull generated by a uniformly distributed sampling in a convex polygon

This article is devoted to the study of the properties of convex hulls generated by independent observations over a random vector that has a uniform distribution in a convex polygon. It is proved in the article that the difference between the perimeters of the support-polygon and the convex hull is asymptotically independent of the number of vertices and the area of the convex hull. In addition, with appropriate centering and normalization in probability, it converges to some random variable, which can be represented as a sum of independent random variables.

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