Preprints

[15] On the geometry of uniform meandric systems (with Ewain Gwynne and Minjae Park).

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 …

[15] On the geometry of uniform meandric systems (with Ewain Gwynne and Minjae Park).Read More »

[14] Permutons, meanders, and SLE-decorated Liouville quantum gravity (with Ewain Gwynne and Xin Sun).

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 …

[14] Permutons, meanders, and SLE-decorated Liouville quantum gravity (with Ewain Gwynne and Xin Sun).Read More »

[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] 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 …

[12] The skew Brownian permuton: a new universality class for random constrained permutations.Read More »