On some properties of vertex processes of random convex hulls.

Consider a convex hull generated by a homogeneous Poisson point process in a cone on the plane. In this paper, we present a result that the area of bounded perimeters of the convex hull and the support boundary of the distribution in the cone is the sum of independent identically distributed random variables. In addition, we prove the central limit theorem for the number of vertices of the convex hull in a cone bounded by a disk of radius T as T → ∞. The known results of [1] coincide with the results obtained in the paper. [ABSTRACT FROM AUTHOR]