# Scaling limits of permutation classes with a finite specification: A dichotomy

@article{Bassino2019ScalingLO, title={Scaling limits of permutation classes with a finite specification: A dichotomy}, author={Fr{\'e}d{\'e}rique Bassino and Mathilde Bouvel and Valentin F{\'e}ray and Lucas Gerin and Mickael Maazoun and Adeline Pierrot}, journal={Advances in Mathematics}, year={2019} }

## 15 Citations

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Random combinatorial structures form an active field of research at the interface between combinatorics and probability theory. From a theoretical point of view, some of the main objectives are to…

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### Baxter permuton and Liouville quantum gravity

- MathematicsProbability Theory and Related Fields
- 2023

The Baxter permuton is a random probability measure on the unit square which describes the scaling limit of uniform Baxter permutations. We ﬁnd an explict formula for the expectation of the Baxter…

### Random cographs: Brownian graphon limit and asymptotic degree distribution

- MathematicsRandom Struct. Algorithms
- 2022

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- 2022

Baxter permutations, plane bipolar orientations, and a specific family of walks in the non-negative quadrant, called \emph{tandem walks}, are well-known to be related to each other through several…

### Convergence law for $231$-avoiding permutations

- Mathematics
- 2022

. We prove that the class of 231-avoiding permutations satisﬁes a convergence law, i.e. that for any ﬁrst-order sentence Ψ, in the language of two total orders, the probability p n, Ψ that a uniform…

### Locally uniform random permutations with large increasing subsequences

- Mathematics
- 2023

We investigate the maximal size of an increasing subset among points randomly sampled from certain probability densities. Kerov and Vershik’s celebrated result states that the largest increasing…

### A decorated tree approach to random permutations in substitution-closed classes

- MathematicsElectronic Journal of Probability
- 2020

We establish a novel bijective encoding that represents permutations as forests of decorated (or enriched) trees. This allows us to prove local convergence of uniform random permutations from…

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