We consider the colored asymmetric simple exclusion process (ASEP) and stochastic six
vertex (S6V) model with fully packed initial conditions; the states of these models can be …

In this text we introduce and analyze families of symmetric functions arising as partition
functions for colored fermionic vertex models associated with the quantized affine Lie …

Recently, there has been much progress in understanding stationary measures for colored
(also called multi-species or multi-type) interacting particle systems, motivated by asymptotic …

Abstract We study Hall–Littlewood polynomials using an integrable lattice model of t-
deformed bosons. Working with row-to-row transfer matrices, we review the construction of …

Recently James Martin introduced {\it multiline queues}, and used them to give a
combinatorial formula for the stationary distribution of the multispecies asymmetric simple …

We show that the quantum R matrix for symmetric tensor representations of U q (A n (1))
satisfies the sum rule required for its stochastic interpretation under a suitable gauge. Its …

We introduce and study several random combinatorial billiard trajectories. Such a system,
which depends on a fixed parameter $ p\in (0, 1) $, models a beam of light that travels in a …

The tetrahedron equation introduced by Zamolodchikov is a three-dimensional
generalization of the Yang–Baxter equation. Several types of solutions to the tetrahedron …

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 …

Starting from an integrable rank-$ n $ vertex model, we construct an explicit family of
partition functions indexed by compositions $\mu=(\mu _1,\dots,\mu _n) $. Using the Yang …