In a surprising sequence of developments, the longest increasing subsequence problem,
originally mentioned as merely a curious example in a 1961 paper, has proven to have deep …

This work is dedicated to $\mathfrak {sl} _ {n+ 1} $-related integrable stochastic vertex
models; we call such models coloured. We prove several results about these models, which …

We discover a new property of the stochastic colored six-vertex model called flip-invariance.
We use it to show that for a given collection of observables of the model, any transformation …

In the multi-type totally asymmetric simple exclusion process (TASEP) on the line, each site
of ℤ is occupied by a particle labeled with some number, and two neighboring particles are …

We formulate and establish symmetries of certain integrable half space models, analogous
to recent results on symmetries for models in a full space. Our starting point is the colored …

We prove a color-position symmetry for a class of ASEP-like interacting particle systems with
discrete time on the one-dimensional lattice. The full space-time inhomogeneity of our …

A sorting network (also known as a reduced decomposition of the reverse permutation) is a
shortest path from $12\cdots n $ to $ n\cdots 21$ in the Cayley graph of the symmetric group …

For ASEP with step initial data and a second class particle started at the origin we prove that
as time goes to infinity the second class particle almost surely achieves a velocity that is …

This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP)
on a segment of length N. Our main result is that for particle densities in (0, 1), the total …

We study an infinite version of the “jeu de taquin” sliding game, which can be thought of as a
natural measure-preserving transformation on the set of infinite Young tableaux equipped …