Year: 2012
Type: preprint
Abstract: We show that we can construct simultaneously all the stable trees as a nested family. More precisely, if $1 < a < a' \leq 2$ 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.
Source: arXiv (Cornell University)
Authors: Curien, Nicolas, Haas, Bénédicte
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W2949785645