The size of components in continuum nearest-neighbor graphs
Probability
2007-05-23 v1
Abstract
We study the size of connected components of random nearest-neighbor graphs with vertex set the points of a homogeneous Poisson point process in . The connectivity function is shown to decay superexponentially, and we identify the exact exponent. From this we also obtain the decay rate of the maximal number of points of a path through the origin. We define the generation number of a point in a component and establish its asymptotic distribution as the dimension tends to infinity.
Keywords
Cite
@article{arxiv.math/0605640,
title = {The size of components in continuum nearest-neighbor graphs},
author = {Iva Kozakova and Ronald Meester and Seema Nanda},
journal= {arXiv preprint arXiv:math/0605640},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/009117905000000729 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)