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math.CO2017
Statistics of the Voronoi cell perimeter in large bi-pointed maps
Emmanuel Guitter
We study the statistics of the Voronoi cell perimeter in large bi-pointed planar quadrangulations. Such maps have two marked vertices at a fixed given distance and their Voron…
math.CO2017
A universal law for Voronoi cell volumes in infinitely large maps
Emmanuel Guitter
We discuss the volume of Voronoi cells defined by two marked vertices picked randomly at a fixed given mutual distance 2s in random planar quadrangulations. We consider the regime…
math.CO2017★ 8 cited
On a conjecture by Chapuy about Voronoi cells in large maps
Emmanuel Guitter
In a recent paper, Chapuy conjectured that, for any positive integer k, the law for the fractions of total area covered by the k Voronoi cells defined by k points picked uniformly…