Bounds to the normal for proximity region graphs

Larry Goldstein 1 Tobias Johnson 1 Raphaël Lachièze-Rey 2
1 University of Southern California
USC - University of Southern California [Los Angeles], Haskins Laboratories
Abstract : In a proximity region graph G in R d , two distinct points x, y of a point process µ are connected when the 'forbidden region' S(x, y) these points determine has empty intersection with µ. The Gabriel graph, where S(x, y) is the open disc with diameter the line segment connecting x and y, is one canonical example. Under broad conditions on the process µ and 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 total length.
Type de document :
Pré-publication, Document de travail
MAP5 2015-37. 2015
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Soumis le : lundi 2 novembre 2015 - 18:32:03
Dernière modification le : mardi 11 octobre 2016 - 14:23:52
Document(s) archivé(s) le : mercredi 3 février 2016 - 11:04:53

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  • HAL Id : hal-01223503, version 1
  • ARXIV : 1510.09188

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Larry Goldstein, Tobias Johnson, Raphaël Lachièze-Rey. Bounds to the normal for proximity region graphs. MAP5 2015-37. 2015. <hal-01223503>

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