Published

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 skew Brownian permutons introduced by Borga (2021), which describe the scaling limit of various types of random pattern-avoiding permutations. Another interesting permuton in our …

[17] Permutons, meanders, and SLE-decorated Liouville quantum gravity (with Ewain Gwynne and Xin Sun). To appear in Journal of the European Mathematical Society (2025)Read More »

We obtain scaling and local limit results for large random Young tableaux of fixed shape via the asymptotic analysis of a determinantal point process due to Gorin and Rahman (2019). More precisely, we prove:   an explicit description of the limiting surface of a uniform random Young tableau of shape , based on solving a complex-valued …

[16] A determinantal point process approach to scaling and local limits of random Young tableaux (with Cédric Boutillier, Valentin Féray and Pierre-Loïc Méliot). Annals of Probability 53 (2025), no. 1, pp. 299-354.Read More »

The Brownian separable permutons are a one-parameter family – indexed by – of universal limits of random constrained permutations. We show that for each , there are explicit constants such that the length of the longest increasing subsequence in a random permutation of size sampled from the Brownian separable permuton is between and with probability …

[15] Power-law bounds for increasing subsequences in Brownian separable permutons and homogeneous sets in Brownian cographons (with William Da Silva and Ewain Gwynne). Advances in Mathematics (2024), Volume 439.Read More »

A meandric system of size is the set of loops formed from two arc diagrams (non-crossing perfect matchings) on , one drawn above the real line and the other below the real line. A uniform random meandric system can be viewed as a random planar map decorated by a Hamiltonian path (corresponding to the real …

[14] On the geometry of uniform meandric systems (with Ewain Gwynne and Minjae Park). Communications in Mathematical Physics (2023), https://doi.org/10.1007/s00220-023-04846-y.Read More »

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). International Mathematics Research Notices (2023), rnad096.Read More »

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). Probability Theory and Related Fields 186 (2023), pp. 1225–1273.Read More »

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 permutations. Proceedings of the London Mathematical Society 126 (2023), no. 6, pp. 1842–1883.Read More »

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 permuton. Electronic Journal of Probability 27 (2022), pp. 1–53.Read More »

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). Discrete Mathematics 346 (2023), no. 2, pp. 113–219.Read More »

Notation: Given , we set and . We also set . The model We consider a league of teams denoted by whose initial random strengths are denoted by . In the league every team plays matches, one against each of the remaining teams . Note that there are in total matches in the league. These …

[8] Quenched law of large numbers and quenched central limit theorem for multi-player leagues with ergodic strengths (with Benedetta Cavalli). Annals of Applied Probability 32 (2022), no. 6, pp. 4398-4425.Read More »