Preprints

Permutons, which are probability measures on the unit square with uniform marginals, are the natural scaling limits for sequences of (random) permutations. We introduce a -dimensional generalization of these measures for all , which we call –dimensional permutons, and extend — from the two-dimensional setting — the theory to prove convergence of sequences of (random) …

[20] High-dimensional permutons: theory and applications (with Andrew Lin).Read More »

We give a sum over weighted planar surfaces formula for Wilson loop expectations in the large- limit of strongly coupled lattice Yang–Mills theory, in any dimension. The weights of each surface are simple and expressed in terms of products of signed Catalan numbers. In establishing our results, the main novelty is to convert a recursive …

[19] Surface sums for lattice Yang–Mills in the large-N limit (with Sky Cao and Jasper Shogren-Knaak).Read More »

Permutons constructed from a Liouville quantum gravity surface and a pair of space-filling Schramm-Loewner evolutions (SLEs) have been shown — or are conjectured — to describe the scaling limit of various natural models of random constrained permutations.  We prove that, in two distinct and natural settings, these permutons uniquely determine, modulo rotation, scaling, translation and …

[18] Reconstructing SLE-decorated Liouville quantum gravity surfaces from random permutons (with Ewain Gwynne).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 »