Open Access
May 2006 Local limit of labeled trees and expected volume growth in a random quadrangulation
Philippe Chassaing, Bergfinnur Durhuus
Ann. Probab. 34(3): 879-917 (May 2006). DOI: 10.1214/009117905000000774


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).


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Philippe Chassaing. Bergfinnur Durhuus. "Local limit of labeled trees and expected volume growth in a random quadrangulation." Ann. Probab. 34 (3) 879 - 917, May 2006.


Published: May 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1102.60007
MathSciNet: MR2243873
Digital Object Identifier: 10.1214/009117905000000774

Primary: 60C05
Secondary: 05C05 , 05C30 , 82B41

Keywords: birth and death process , expected volume growth , Galton–Watson trees , quadrangulation , quantum gravity , Random surface , well-labeled trees

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 3 • May 2006
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