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

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 (2d/π)^1/2 + O(1/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.

The paper is published in Discrete and Computational Geometry and you can find here.

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