Open Access
2020 A decorated tree approach to random permutations in substitution-closed classes
Jacopo Borga, Mathilde Bouvel, Valentin Féray, Benedikt Stufler
Electron. J. Probab. 25: 1-52 (2020). DOI: 10.1214/20-EJP469


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. "A decorated tree approach to random permutations in substitution-closed classes." Electron. J. Probab. 25 1 - 52, 2020.


Received: 15 April 2019; Accepted: 26 May 2020; Published: 2020
First available in Project Euclid: 20 June 2020

zbMATH: 07225521
MathSciNet: MR4115736
Digital Object Identifier: 10.1214/20-EJP469

Primary: 05A05 , 60C05

Keywords: Galton–Watson trees , Local and scaling limits , permutation patterns

Vol.25 • 2020
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