Scaling limits for a family of unrooted trees

Wang, Minmin (2016) Scaling limits for a family of unrooted trees. Latin American Journal of Probability and Mathematical Statistics, 13 (2). pp. 1039-1067. ISSN 1980-0436

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Abstract

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 integers whose mean is bounded by 1; then the μp-weight of a plane tree t is defined as Π μ_p(degree(v) − 1), where the product is over the set of vertices v of t. We study the random plane tree T_p which has a fixed diameter p and is sampled according to probabilities proportional to these μ_p-weights. We prove that, under the assumption that the sequence of laws μ_p, p ≥ 1, belongs to the domain of attraction of an infinitely divisible law, the scaling limits of (T_p , p ≥ 1) are random compact real trees called the unrooted Lévy trees, which have been introduced in Duquesne and Wang (2016+).

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Related URLs:
Depositing User: Minmin Wang
Date Deposited: 12 Feb 2019 12:50
Last Modified: 02 Jul 2019 13:02
URI: http://sro.sussex.ac.uk/id/eprint/81912

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