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, to appear, arXiv.
• A decorated tree approach to random permutations in substitution-closed classes , with Jacopo Borga, Mathilde Bouvel and Benedikt Stufler.
Preprint, arXiv.
• Scaling limits of permutation classes with a finite specification: a dichotomy, with Frédérique Bassino, Mathilde Bouvel, Lucas Gerin, Mickaël Maazoun and Adeline Pierrot.
Preprint, arXiv.