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The Brownian limit of separable permutations

Probability 2018-10-18 v3 Combinatorics

Abstract

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".

Keywords

Cite

@article{arxiv.1602.04960,
  title  = {The Brownian limit of separable permutations},
  author = {Frédérique Bassino and Mathilde Bouvel and Valentin Féray and Lucas Gerin and Adeline Pierrot},
  journal= {arXiv preprint arXiv:1602.04960},
  year   = {2018}
}

Comments

45 pages, 14 figures, incorporating referee's suggestions

R2 v1 2026-06-22T12:51:03.720Z