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

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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 $Θ(r^4)$.
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)

Keywords

Probability, Combinatorics, 60C05 (Primary) 05C30, 05C05, 82B41 (Secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/99913

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0311532
 http://arxiv.org/abs/math/0311532
 Annals of Probability 2006, Vol. 34, No. 3, 879-917
 doi:10.1214/009117905000000774

Collections

arXiv