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July 2018 The Brownian limit of separable permutations
Frédérique Bassino, Mathilde Bouvel, Valentin Féray, Lucas Gerin, Adeline Pierrot
Ann. Probab. 46(4): 2134-2189 (July 2018). DOI: 10.1214/17-AOP1223

Abstract

We study uniform random 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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Frédérique Bassino. Mathilde Bouvel. Valentin Féray. Lucas Gerin. Adeline Pierrot. "The Brownian limit of separable permutations." Ann. Probab. 46 (4) 2134 - 2189, July 2018. https://doi.org/10.1214/17-AOP1223

Information

Received: 1 April 2016; Revised: 1 February 2017; Published: July 2018
First available in Project Euclid: 13 June 2018

zbMATH: 06919021
MathSciNet: MR3813988
Digital Object Identifier: 10.1214/17-AOP1223

Subjects:
Primary: 05A05, 60C05

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 4 • July 2018
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