The stable trees are nested
Probability
2012-07-24 v1
Abstract
We show that we can construct simultaneously all the stable trees as a nested family. More precisely, if we prove that hidden inside any a-stable we can find a version of an a'-stable tree rescaled by an independent Mittag-Leffler type distribution. This tree can be explicitly constructed by a pruning procedure of the underlying stable tree or by a modification of the fragmentation associated with it. Our proofs are based on a recursive construction due to Marchal which is proved to converge almost surely towards a stable tree.
Keywords
Cite
@article{arxiv.1207.5418,
title = {The stable trees are nested},
author = {Nicolas Curien and Bénédicte Haas},
journal= {arXiv preprint arXiv:1207.5418},
year = {2012}
}