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


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

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.

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Uncontrolled Keywords:Statistics, Probability and Uncertainty, Statistics and Probability
Language:English
Date:1 January 2020
Deposited On:06 Nov 2020 12:33
Last Modified:07 Nov 2020 21:01
Publisher:Institute of Mathematical Statistics
ISSN:1083-6489
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/20-ejp469

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