On the Brownian separable permuton

Abstract : 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.
Type de document :
Pré-publication, Document de travail
2017
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-01651215
Contributeur : Mickaël Maazoun <>
Soumis le : mardi 28 novembre 2017 - 17:52:16
Dernière modification le : jeudi 11 janvier 2018 - 06:12:31

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permuton.pdf
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  • HAL Id : ensl-01651215, version 1
  • ARXIV : 1711.08986

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Mickaël Maazoun. On the Brownian separable permuton. 2017. 〈ensl-01651215〉

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