Annals of Probability

The Brownian limit of separable permutations

Frédérique Bassino, Mathilde Bouvel, Valentin Féray, Lucas Gerin, and Adeline Pierrot

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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”.

Article information

Ann. Probab., Volume 46, Number 4 (2018), 2134-2189.

Received: April 2016
Revised: February 2017
First available in Project Euclid: 13 June 2018

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Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability 05A05: Permutations, words, matrices

Permutation patterns Brownian excursion permutons


Bassino, Frédérique; Bouvel, Mathilde; Féray, Valentin; Gerin, Lucas; Pierrot, Adeline. The Brownian limit of separable permutations. Ann. Probab. 46 (2018), no. 4, 2134--2189. doi:10.1214/17-AOP1223.

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