1. Tessellations of random maps of arbitrary genus
- Author
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Grégory Miermont, Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), and ANR-08-BLAN-0190,A3,Arbres Aléatoires (continus) et Applications(2008)
- Subjects
General Mathematics ,60C05 ,05C30 ,60F05 ,Computer Science::Computational Geometry ,01 natural sciences ,scaling limits ,010104 statistics & probability ,asymptotic enumeration ,Mathematics::Probability ,Computer Science::Discrete Mathematics ,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] ,Scale size ,FOS: Mathematics ,Mathematics - Combinatorics ,0101 mathematics ,Mathematics ,Mathematics::Combinatorics ,010102 general mathematics ,Probability (math.PR) ,random snakes ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,Random maps ,Combinatorics (math.CO) ,Humanities ,Mathematics - Probability ,geodesics - Abstract
We investigate Voronoi-like tessellations of bipartite quadrangulations on surfaces of arbitrary genus, by using a natural generalization of a bijection of Marcus and Schaeffer allowing to encode such structures into labeled maps with a fixed number of faces. We investigate the scaling limits of the latter. Applications include asymptotic enumeration results for quadrangulations, and typical metric properties of randomly sampled quadrangulations. In particular, we show that scaling limits of these random quadrangulations are such that almost every pair of points are linked by a unique geodesic., 58pp, 6 figures. One figure added, minor corrections
- Published
- 2007