The permuton limit of random recursive separable permutations
Confluentes Mathematici, Volume 15 (2023), pp. 45-82.

We introduce and study a simple Markovian model of random separable permutations. Our first main result is the almost sure convergence of these permutations towards a random limiting object in the sense of permutons, which we call the recursive separable permuton. We then prove several results on this new limiting object: a characterization of its distribution via a fixed-point equation, a combinatorial formula for its expected pattern densities, an explicit integral formula for its intensity measure, and lastly, we prove that its distribution is absolutely singular with respect to that of the Brownian separable permuton, which is the large size limit of uniform random separable permutations.

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DOI: 10.5802/cml.92
Classification: 60C05, 05A05
Keywords: permutons, permutation patterns, random combinatorial structures
Valentin Féray 1; Kelvin Rivera-Lopez 2

1 Université de Lorraine, CNRS, IECL, F-54000, Nancy, France
2 Department of Mathematics, Gonzaga University, Washington State, USA.
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Valentin Féray; Kelvin Rivera-Lopez. The permuton limit of random recursive separable permutations. Confluentes Mathematici, Volume 15 (2023), pp. 45-82. doi : 10.5802/cml.92. https://cml.centre-mersenne.org/articles/10.5802/cml.92/

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