Preprints

[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 »

[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 »

[9] The feasible regions for consecutive patterns of pattern-avoiding permutations (with Raul Penaguiao)

We study the feasible region for consecutive patterns of pattern-avoiding permutations. More precisely, given a family of permutations avoiding a fixed set of patterns, we study the limit of proportions of consecutive patterns on large permutations of . These limits form a region, which we call the pattern-avoiding feasible region for . We show that, …

[9] The feasible regions for consecutive patterns of pattern-avoiding permutations (with Raul Penaguiao)Read More »