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arXiv · 1904.07135

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

Jacopo Borga·Mathilde Bouvel·Valentin Féray·Benedikt Stufler
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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.

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Jacopo Borga, Mathilde Bouvel, Valentin Féray, Benedikt Stufler. 2019-04-15. A decorated tree approach to random permutations in substitution-closed classes. https://doi.org/10.1214/20-ejp469

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