A universal law for Voronoi cell volumes in infinitely large maps
| Autor: | Emmanuel Guitter |
|---|---|
| Přispěvatelé: | Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), ANR-14-CE25-0014,GRAAL,GRaphes et Arbres ALéatoires(2014) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
media_common.quotation_subject [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] FOS: Physical sciences Universal law Computer Science::Computational Geometry 01 natural sciences Planar 0103 physical sciences [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] FOS: Mathematics Mathematics - Combinatorics 0101 mathematics 010306 general physics Mathematical Physics random graphs media_common Mathematics Finite volume method Laplace transform 010102 general mathematics Mathematical analysis Statistical and Nonlinear Physics Mathematical Physics (math-ph) 16. Peace & justice Infinity networks Probability distribution Combinatorics (math.CO) rigorous results in statistical mechanics Statistics Probability and Uncertainty exact results Voronoi diagram Volume (compression) |
| Zdroj: | Journal of Statistical Mechanics: Theory and Experiment Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2018, 18, pp.013205. ⟨10.1088/1742-5468/aa9db4⟩ Journal of Statistical Mechanics: Theory and Experiment, 2018, 18, pp.013205. ⟨10.1088/1742-5468/aa9db4⟩ |
| ISSN: | 1742-5468 |
| DOI: | 10.1088/1742-5468/aa9db4⟩ |
| Popis: | 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 where the mutual distance 2s 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. 23 pages, 6 figures |
| Databáze: | OpenAIRE |
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