A decorated tree approach to random permutations in substitution-closed classes
Probability
2020-07-01 v2 Combinatorics
Abstract
We establish a novel bijective encoding that represents permutations as forests of decorated (or enriched) trees. This allows us to prove local convergence of uniform random permutations from substitution-closed classes satisfying a criticality constraint. It also enables us to reprove and strengthen permuton limits for these classes in a new way, that uses a semi-local version of Aldous' skeleton decomposition for size-constrained Galton--Watson trees.
Keywords
Cite
@article{arxiv.1904.07135,
title = {A decorated tree approach to random permutations in substitution-closed classes},
author = {Jacopo Borga and Mathilde Bouvel and Valentin Féray and Benedikt Stufler},
journal= {arXiv preprint arXiv:1904.07135},
year = {2020}
}
Comments
New version including referee's corrections, accepted for publication in Electronic Journal of Probability