# The skew Brownian permuton: a new universality class for random constrained permutations

@inproceedings{Borga2021TheSB, title={The skew Brownian permuton: a new universality class for random constrained permutations}, author={Jacopo Borga}, year={2021} }

We construct a new family of random permutons, called skew Brownian permuton, which describes the limits of various models of random constrained permutations. This family is parametrized by two real parameters. For a specific choice of the parameters, the skew Brownian permuton coincides with the Baxter permuton, i.e. the permuton limit of Baxter permutations. We prove that for another specific choice of the parameters, the skew Brownian permuton coincides with the biased Brownian separable…

## 6 Citations

### The permuton limit of strong-Baxter and semi-Baxter permutations is the skew Brownian permuton

- MathematicsElectronic Journal of Probability
- 2022

We recently introduced a new universal family of permutons, depending on two parameters, called skew Brownian permuton. For some specific choices of the parameters, the skew Brownian permuton…

### 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…

### Permutons, meanders, and SLE-decorated Liouville quantum gravity

- Mathematics
- 2022

We study a class of random permutons which can be constructed from a pair of space-ﬁlling Schramm-Loewner evolution (SLE) curves on a Liouville quantum gravity (LQG) surface. This class includes the…

### Large deviation principle for random permutations

- Mathematics, Computer Science
- 2022

A large deviation principle for random permutations induced by probability measures of the unit square is derived and some properties of conditionally constant permutons are described with respect to inversions, which lead to a new notion ofpermutons, which generalizes both pattern-avoiding and pattern-packing permutations.

### Quantum triangles and imaginary geometry flow lines

- Mathematics, Physics
- 2022

We define a three-parameter family of random surfaces in Liouville quantum gravity (LQG) which can be viewed as the quantum version of triangles. These quantum triangles are natural in two senses.…

### On the enumeration of plane bipolar posets and transversal structures

- MathematicsTrends in Mathematics
- 2021

It is shown that plane bipolar posets and transversal structures can be set in correspondence to certain (weighted) models of quadrant walks, via suitable specializations of a bijection due to Kenyon, Miller, Sheffield and Wilson.

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