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Article Dans Une Revue Annals of Probability Année : 2006

Local limit of labeled trees and expected volume growth in a random quadrangulation

Philippe Chassaing
Bergfinnur Durhuus
  • Fonction : Auteur

Résumé

Exploiting a bijective correspondence between planar quadrangulations and well-labeled trees, we define an ensemble of infinite surfaces as a limit of uniformly distributed ensembles of quadrangulations of fixed finite volume. The limit random surface can be described in terms of a birth and death process and a sequence of multitype Galton--Watson trees. As a consequence, we find that the expected volume of the ball of radius $r$ around a marked point in the limit random surface is $\Theta(r^4)$.

Dates et versions

hal-00137910 , version 1 (22-03-2007)

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Philippe Chassaing, Bergfinnur Durhuus. Local limit of labeled trees and expected volume growth in a random quadrangulation. Annals of Probability, 2006, 34 numéro 3, pp.879-917. ⟨10.1214/009117905000000774⟩. ⟨hal-00137910⟩
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