Preprints

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

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).Read More »

[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.

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 »

[15] 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 …

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