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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2018

A universal law for Voronoi cell volumes in infinitely large maps

Résumé

We discuss the volume of Voronoi cells defined by two marked vertices picked randomly at a fixed given mutual distance 2$s$ in random planar quadrangulations. We consider the regime where the mutual distance 2$s$ is kept finite while the total volume of the quadrangulation tends to infinity. In this regime, exactly one of the Voronoi cells keeps a finite volume, which scales as $s^4$ for large $s$. We analyze the universal probability distribution of this, properly rescaled, finite volume and present an explicit formula for its Laplace transform.
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Dates et versions

hal-01549001 , version 1 (28-06-2017)

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Emmanuel Guitter. A universal law for Voronoi cell volumes in infinitely large maps. Journal of Statistical Mechanics: Theory and Experiment, 2018, 18, pp.013205. ⟨10.1088/1742-5468/aa9db4⟩. ⟨hal-01549001⟩
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