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Expected Length of the Voronoi Path in a High Dimensional Poisson-Delaunay Triangulation

Abstract : Let X be a d dimensional Poisson point process. We prove that the expected length of the Voronoi path between two points at distance 1 in the Delaunay triangulation associated with X is sqrt(2d/π) + O(d^(−1/2) when d → ∞. In any dimension, we also provide a precise interval containing the actual value; in 3D the expected length is between 1.4977 and 1.50007.
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Submitted on : Sunday, February 26, 2017 - 7:32:49 PM
Last modification on : Friday, February 4, 2022 - 9:00:13 AM
Long-term archiving on: : Saturday, May 27, 2017 - 12:33:05 PM

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Pedro Machado Manhães de Castro, Olivier Devillers. Expected Length of the Voronoi Path in a High Dimensional Poisson-Delaunay Triangulation. Discrete and Computational Geometry, Springer Verlag, 2018, 60 (1), pp.200--219. ⟨10.1007/s00454-017-9866-y⟩. ⟨hal-01477030⟩

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