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The Brownian limit of separable permutations

Abstract : We 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 pattern in 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".
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Submitted on : Monday, June 18, 2018 - 11:47:42 PM
Last modification on : Saturday, May 1, 2021 - 3:47:10 AM

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Frédérique Bassino, Mathilde Bouvel, Valentin Féray, Lucas Gerin, Adeline Pierrot. The Brownian limit of separable permutations. Annals of Probability, Institute of Mathematical Statistics, 2018, 46 (4), pp.2134 - 2189. ⟨10.1214/17-AOP1223⟩. ⟨hal-01818309⟩



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