The Brownian limit of separable permutations
Frédérique Bassino, Mathilde Bouvel, Valentin Féray, Lucas Gerin, Adeline Pierrot · Zurich Open Repository and Archive (University of Zurich) · 2018
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".