The size of components in continuum nearest-neighbor graphs

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dc.creatorKozakova, Iva
dc.creatorMeester, Ronald
dc.creatorNanda, Seema
dc.date2006-05-24
dc.date.accessioned2026-07-07T07:14:30Z
dc.date.available2026-07-07T07:14:30Z
dc.descriptionWe study the size of connected components of random nearest-neighbor graphs with vertex set the points of a homogeneous Poisson point process in ${\mathbb{R}}^d$. 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 $d$ tends to infinity.
dc.descriptionPublished 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)
dc.identifierhttps://arxiv.org/abs/math/0605640
dc.identifierhttp://arxiv.org/abs/math/0605640
dc.identifierAnnals of Probability 2006, Vol. 34, No. 2, 528-538
dc.identifierdoi:10.1214/009117905000000729
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112899
dc.subjectProbability
dc.subject60K35, 60G55, 60D05 (Primary)
dc.titleThe size of components in continuum nearest-neighbor graphs
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