High-dimensional permutons: Theory and applications

Permutons, which are probability measures on [0, 1]^2 with uniform marginals, are the natural scaling limits for sequences of (random) permutations. In particular, various classes of permutations arising from combinatorics and pattern avoidance have been shown to converge to universal permuton limits with close connections to random geometry. I will describe a d-dimensional generalization of these measures and determine the "d-permuton" limits for two natural families of high-dimensional permutations, called Schnyder wood permutations and d-separable permutations.

This talk is based on joint work with Jacopo Borga.