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

• Philippe Chassaing ^[2] ; Bergfinnur Durhuus ^[1]
  1. [1] University of Copenhagen

     University of Copenhagen

     Dinamarca

     
  2. [2] Université H Poincaré-Nancy
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 34, Nº. 3, 2006, págs. 879-917
• Idioma: inglés
• DOI: 10.1214/009117905000000774
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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 Θ(r4).