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

• 成果类型: Article
• 署名作者: Chassaing, Philippe; Durhuus, Bergfinnur
• 署名单位: Universite de Lorraine; University of Copenhagen; University of Copenhagen
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000774
• 发表日期: 2006
• 页码: 879-917
• 关键词: quantum-gravity; surface models; planar maps

摘要

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)).