A decorated tree approach to random permutations in substitution-closed classes

Borga, Jacopo; Bouvel, Mathilde; Feray, Valentin; Stufler, Benedikt (2020): A decorated tree approach to random permutations in substitution-closed classes. In: Electronic Journal of Probability, Vol. 25, 67

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1083-6489
• Language: English