Article

On some properties of vertex processes of random convex hulls

Shakir Kasimovich FormanovNational University of Uzbekistan named after Mirzo Ulugbek, 100174, University str 4, Olmazor district, Tashkent, UzbekistanIsakjan KhamdamovNational University of Uzbekistan named after Mirzo Ulugbek, 100174, University str 4, Olmazor district, Tashkent, Uzbekistan

AIP conference proceedingsjournal2021en

ABI

Abstract

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.

Topics

Point processes and geometric inequalities Geometric Analysis and Curvature Flows Diffusion and Search Dynamics

Identifiers

DOI: 10.1063/5.0057259

Citations and references

Cited by 1 14 references

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