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The Brownian limit of separable permutations


Bassino, Frédérique; Bouvel, Mathilde; Féray, Valentin; Gerin, Lucas; Pierrot, Adeline (2018). The Brownian limit of separable permutations. The Annals of Probability, 46(4):2134-2189.

Abstract

We study uniform random permutations in an important class of pattern-avoiding permutations: the separable permutations. We describe the asymptotics of the number of occurrences of any fixed given pattern in such a random permutation in terms of the Brownian excursion. In the recent terminology of permutons, our work can be interpreted as the convergence of uniform random separable permutations towards a "Brownian separable permuton".

Abstract

We study uniform random permutations in an important class of pattern-avoiding permutations: the separable permutations. We describe the asymptotics of the number of occurrences of any fixed given pattern in such a random permutation in terms of the Brownian excursion. In the recent terminology of permutons, our work can be interpreted as the convergence of uniform random separable permutations towards a "Brownian separable permuton".

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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:510 Mathematics
Uncontrolled Keywords:Statistics, Probability and Uncertainty, Statistics and Probability
Language:English
Date:2018
Deposited On:19 Jan 2018 11:28
Last Modified:19 Aug 2018 13:01
Publisher:Institute of Mathematical Statistics
ISSN:0091-1798
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/17-AOP1223
Official URL:http://imstat.org/aop/
Other Identification Number:arXiv:1602.04960

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