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.