Bounds to the normal for proximity region graphs

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Goldstein, Larry¹  Johnson, Tobias¹  Lachieze-Rey, Raphael² 

[1] Univ Southern Calif, Los Angeles, CA 90089 USA

[2] Univ Paris 05, Sorbonne Paris Cite, Paris, France

关键词: Forbidden region graph;    Berry-Esseen bounds;    Stabilization;    Poisson functionals;   

DOI  :  10.1016/j.spa.2017.07.002

来源: Elsevier

【 摘 要 】

In a proximity region graph G in R-d, two distinct points x, y of a point process mu are connected when the 'forbidden region' S(x, y) these points determine has empty intersection with mu. The Gabriel graph, where S(x, y) is the open disk with diameter the line segment connecting x and y, is one canonical example. When mu is a Poisson or binomial process, under broad conditions on the regions S(x, y), bounds on the Kolmogorov and Wasserstein distances to the normal are produced for functionals of g, including the total number of edges and the total length. Variance lower bounds, not requiring strong stabilization, are also proven to hold for a class of such functionals. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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