This represents the diagrams of two large separable permutations, taken uniformly at random: for each \(i\),
there is a dot at coordinates \( (i,\sigma(i))\). It converges towards a Brownian limiting object,
that we called Brownian separable permuton. The same limit arises for uniform random permutations
in a large family of permutation classes.
See details in the following articles:
- The Brownian limit of separable permutations, with Frédérique Bassino, Mathilde Bouvel, Lucas Gerin and Adeline Pierrot.
Annals of Probability, 46 (4), pp. 2134-2189, 2018,
arXiv.
- Universal limits of substitution-closed permutation classes,
with Frédérique Bassino, Mathilde Bouvel, Lucas Gerin, Mickaël Maazoun and Adeline Pierrot.
Journal of European Mathematical Society, 22 (11), pp. 3565–3639, 2020, arXiv.
- A decorated tree approach to random permutations in substitution-closed classes,
with Jacopo Borga, Mathilde Bouvel, and Benedikt Stufler.
Electronic Journal of Probability, 25, paper no. 67, pp. 1-52, 2020, arXiv.
- Scaling limits of permutation classes with a finite specification: a dichotomy,
with Frédérique Bassino, Mathilde Bouvel, Lucas Gerin, Mickaël Maazoun and Adeline Pierrot.
Advances in Mathematics, vol. 405, Article 108513, 2022, arXiv.