Jacopo

[13] Large deviation principle for random permutations (with Sayan Das, Sumit Mukherjee, Peter Winkler)

We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called μ-random permutations. We also introduce and study a new general class of models of random permutations, called Gibbs permutation models, which combines and generalizes μ-random permutations and the celebrated Mallows model for …

[13] Large deviation principle for random permutations (with Sayan Das, Sumit Mukherjee, Peter Winkler)Read More »

[12] Baxter permuton and Liouville quantum gravity (with Nina Holden, Xin Sun, and Pu Yu)

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 permuton, i.e. the density of its intensity measure. This answers a question of Dokos and Pak (2014). We also prove that all pattern …

[12] Baxter permuton and Liouville quantum gravity (with Nina Holden, Xin Sun, and Pu Yu)Read More »

The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravity

Consider a large random permutation satisfying some constraints or biased according to some statistics. What does it look like? In this seminar we make sense of this question introducing the notion of permuton. Permuton convergence has been established for several models of random permutations in various works: we give an overview of some of these …

The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravityRead More »

The skew Brownian permuton

Consider a large random permutation satisfying some constraints or biased according to some statistics. What does it look like? In this seminar we make sense of this question introducing the notion of permutons. Permuton convergence has been established for several models of random permutations in various works: we give an overview of some of these results, …

The skew Brownian permutonRead More »

The skew Brownian permuton

The skew Brownian permuton is a universal family of limiting permutons introduced in this work. Here we collect some simulations of the skew Brownian permuton  for different values of the parameters and . In every row there are five simulations of  and at the end there is the corresponding two-dimensional Brownian excursion of correlation  in the non-negative …

The skew Brownian permutonRead More »

[11] The skew Brownian permuton: a new universality class for random constrained permutations

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 …

[11] The skew Brownian permuton: a new universality class for random constrained permutationsRead More »

[10] The permuton limit of strong-Baxter and semi-Baxter permutations is the skew Brownian permuton

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 coincides with some previously studied permutons: the biased Brownian separable permuton and the Baxter permuton. The latter two permutons are degenerate cases of the skew Brownian permuton. In …

[10] The permuton limit of strong-Baxter and semi-Baxter permutations is the skew Brownian permutonRead More »