Rate of Poisson approximation for nearest neighbor counts in large-dimensional Poisson point processes

• Published in: Statistics & probability letters Vol. 92; pp. 143 - 147
• Main Author: Yao, Yi-Ching
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2014
• Subjects: Total variation distance; Typical cell; Typical point; Voronoi tessellation; secondary; Typical cell; Voronoi tessellation; Typical point; Total variation distance; primary

Consider two independent homogeneous Poisson point processes Π of intensity λ and Π′ of intensity λ′ in d-dimensional Euclidean space. Let qk,d, k=0,1,…, be the fraction of Π-points which are the nearest Π-neighbor of precisely k   Π′-points. It is known that as d→∞, the qk,d converge to the Poisson...