文章基本信息

标题：Scaling limits for a family of unrooted trees
本地全文：下载
作者：Minmin Wang
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2016
卷号：XIII
期号：2
页码：1039-1067
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We introduce weights on the unrooted unlabelled plane trees as follows:for each p ≥ 1, let μp be a probability measure on the set of nonnegative integerswhose mean is bounded by 1; then the μp-weight of a plane tree t is defined asμp(degree(v) − 1), where the product is over the set of vertices v of t. Westudy the random plane tree Tp which has a fixed diameter p and is sampledaccording to probabilities proportional to these μp-weights. We prove that, underthe assumption that the sequence of laws μp, p ≥ 1, belongs to the domain ofattraction of an infinitely divisible law, the scaling limits of (Tp, p ≥ 1) are randomcompact real trees called the unrooted L´evy trees, which have been introduced inDuquesne and Wang (2016+).
关键词：Random tree; unlabelled unrooted plane tree; L´evy trees; height;process; diameter.