Weak Laws in Geometric Probability

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dc.creatorPenrose, Mathew D.
dc.creatorYukich, J. E.
dc.date2001-07-20
dc.date.accessioned2026-07-07T04:42:40Z
dc.date.available2026-07-07T04:42:40Z
dc.descriptionUsing a coupling argument, we establish a general weak law of large numbers for functionals of binomial point processes in d-dimensional space, with a limit that depends explicitly on the (possibly non-uniform) density of the point process. The general result is applied to the minimal spanning tree, the k-nearest neighbors graph, the Voronoi graph, and the sphere of influence graph. Functionals of interest include total edge length with arbitrary weighting, number of vertices of specifed degree, and number of components. We also obtain weak laws for functionals of marked point processes, including statistics of Boolean models.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/math/0107149
dc.identifierhttp://arxiv.org/abs/math/0107149
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61878
dc.subjectProbability
dc.subject60D05 (Primary) 60F25 (Secondary)
dc.titleWeak Laws in Geometric Probability
dc.typetext

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