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 …
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 …
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 …
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 …
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 …