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Scaling limits for a family of unrooted trees
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 ? 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+).
History
Publication status
- Published
File Version
- Published version
Journal
Latin American Journal of Probability and Mathematical StatisticsISSN
1980-0436Publisher
AleaPublisher URL
Issue
2Volume
13Page range
1039-1067Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes