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Stretch factor in a planar Poisson–Delaunay triangulation with a large intensity

  • Nicolas Chenavier (a1) and Olivier Devillers (a2)
Abstract

Let X := X n ∪ {(0, 0), (1, 0)}, where X n is a planar Poisson point process of intensity n. We provide a first nontrivial lower bound for the distance between the expected length of the shortest path between (0, 0) and (1, 0) in the Delaunay triangulation associated with X when the intensity of X n goes to ∞. Simulations indicate that the correct value is about 1.04. We also prove that the expected length of the so-called upper path converges to 35 / 3π2, yielding an upper bound for the expected length of the smallest path.

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Corresponding author
* Postal address: LMPA Joseph Liouville, Université du Littoral Côte d'Opale, 50 rue Ferdinand Buisson, BP 699, 62228 Calais Cedex, France. Email address: nicolas.chenavier@univ-littoral.fr
** Postal address: Université de Lorraine, 615 rue du Jardin Botanique, B.P. 101, 54602 Villers-lès-Nancy Cedex, France. Email address: olivier.devillers@inria.fr
References
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
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