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The Brownian limit of separable permutations

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arxiv 1602.04960 v3 pith:G6CQFZ5W submitted 2016-02-16 math.PR math.CO

Frédérique Bassino , Mathilde Bouvel , Valentin Féray , Lucas Gerin , Adeline Pierrot This is my paper · ORCID
classification math.PRmath.CO
keywords permutationsseparablebrownianrandomuniformasymptoticsclassconvergence
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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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  1. The longest increasing subsequence of Brownian separable permutons

    math.PR 2025-06 accept novelty 8.0 of 10

    For permutations sampled from the Brownian separable permuton, LIS(σ_n)/n^{α(p)} converges almost surely to a positive finite random variable, and α(p) is the explicit solution of a Gamma-function equation.

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