# 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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