Brownian separable permuton Brownian separable permuton

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: