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).
Publié le : 2006-05-14
Classification:
Random surface,
quadrangulation,
expected volume growth,
well-labeled trees,
Galton–Watson trees,
birth and death process,
quantum gravity,
60C05,
05C30,
05C05,
82B41
@article{1151418487,
author = {Chassaing, Philippe and Durhuus, Bergfinnur},
title = {Local limit of labeled trees and expected volume growth in a random quadrangulation},
journal = {Ann. Probab.},
volume = {34},
number = {1},
year = {2006},
pages = { 879-917},
language = {en},
url = {http://dml.mathdoc.fr/item/1151418487}
}
Chassaing, Philippe; Durhuus, Bergfinnur. Local limit of labeled trees and expected volume growth in a random quadrangulation. Ann. Probab., Tome 34 (2006) no. 1, pp. 879-917. http://gdmltest.u-ga.fr/item/1151418487/