Preprints

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 …

[17] A determinantal point process approach to scaling and local limits of random Young tableaux (with Cédric Boutillier, Valentin Féray and Pierre-Loïc Méliot). To appear in Annals of Probability.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 …

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

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