标号树的局部极限与随机四角化的期望体积增长
概率论
2007-05-23 v3 组合数学
摘要
利用平面四角化与良标号树之间的双射对应关系，我们将无限曲面的集合定义为固定有限体积四角化一致分布集合的极限。该极限随机曲面可用一个生灭过程与一列多类型Galton–Watson树描述。作为推论，我们发现极限随机曲面中围绕标记点的半径的球之期望体积为。
引用
@article{arxiv.math/0311532,
title = {Local limit of labeled trees and expected volume growth in a random quadrangulation},
author = {Philippe Chassaing and Bergfinnur Durhuus},
journal= {arXiv preprint arXiv:math/0311532},
year = {2007}
}
备注
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)