Preprints

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 …

[16] Power-law bounds for increasing subsequences in Brownian separable permutons and homogeneous sets in Brownian cographons (with William Da Silva and Ewain Gwynne).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 …

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

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 »