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Scaling limits for a family of unrooted trees

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posted on 2023-06-09, 16:51 authored by Minmin WangMinmin Wang
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 Statistics

ISSN

1980-0436

Publisher

Alea

Issue

2

Volume

13

Page range

1039-1067

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2019-02-12

First Open Access (FOA) Date

2019-02-12

First Compliant Deposit (FCD) Date

2019-02-11

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