The Brownian limit of separable permutations

International audienceWe study random uniform 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 patternin 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"