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arXiv:math/0311532 [math.PR]AbstractReferencesReviewsResources

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

Philippe Chassaing, Bergfinnur Durhuus

Published 2003-11-28, updated 2006-06-29Version 3

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 $\Theta(r^4)$.

Comments: Published at http://dx.doi.org/10.1214/009117905000000774 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Probability 2006, Vol. 34, No. 3, 879-917
Categories: math.PR, math.CO
Subjects: 60C05, 05C30, 05C05, 82B41
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