On the connectivity of the Poisson process on fractals

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For a measure mu supported on a compact connected subset of a Euclidean space which satisfies a uniform d-dimensional decay of the volume of balls we show that the maximal edge in the minimum spanning tree of n indepndent samples from mu is, with high probability (log n/n)^(1/d).
5 pages

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Probability, 28A80, 60D05, 60K35

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http://salesiana.dossiersoluciones.com/handle/123456789/111533

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0604261
 http://arxiv.org/abs/math/0604261

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arXiv