On the Brownian separable permuton - ENS de Lyon - École normale supérieure de Lyon
Article Dans Une Revue Combinatorics, Probability and Computing Année : 2020

On the Brownian separable permuton

Mickaël Maazoun

Résumé

The Brownian separable permuton is a random probability measure on the unit square, which was introduced by Bassino, Bouvel, Féray, Gerin, Pierrot (2016) as the scaling limit of the diagram of the uniform separable permutation as size grows to infinity. We show that, almost surely, the permuton is the pushforward of the Lebesgue measure on the graph of a random measure-preserving function associated to a Brownian excursion whose strict local minima are decorated with i.i.d. signs. As a consequence, its support is almost surely totally disconnected, has Hausdorff dimension one, and enjoys self-similarity properties inherited from those of the Brownian excursion. The density function of the averaged permuton is computed and a connection with the shuffling of the Brownian continuum random tree is explored.
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Dates et versions

ensl-01651215 , version 1 (28-11-2017)
ensl-01651215 , version 2 (19-09-2020)

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Mickaël Maazoun. On the Brownian separable permuton. Combinatorics, Probability and Computing, 2020, 29 (2), pp.241-266. ⟨10.1017/S0963548319000300⟩. ⟨ensl-01651215v2⟩
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