We study random permutations arising from reduced pipe dreams. Our main model is
motivated by Grothendieck polynomials with parameter $\beta= 1$ arising in K-theory of the …

We establish a novel bijective encoding that represents permutations as forests of decorated
(or enriched) trees. This allows us to prove local convergence of uniform random …

The Brownian separable permuton is a random probability measure on the unit square,
which was introduced by Bassino, Bouvel, Féray, Gerin and Pierrot (2016) as the scaling …

We consider uniform random permutations in classes having a finite combinatorial
specification for the substitution decomposition. These classes include (but are not limited …

We investigate the maximal size of an increasing subset among points randomly sampled
from certain probability densities. Kerov and Vershik's celebrated result states that the …

We derive a large deviation principle for random permutations induced by probability
measures of the unit square, called permutons. These permutations are called-random …

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 …

We construct a new family of random permutons, called skew Brownian permuton, which
describes the limits of several models of random constrained permutations. This family is …

Baxter permutations, plane bipolar orientations, and a specific family of walks in the
nonnegative quadrant, called tandem walks, are well-known to be related to each other …

We describe the limit (for two topologies) of large uniform random square permutations, that
is, permutations where every point is a record. The starting point for all our results is a …