We consider the general problem of determining the steady state of stochastic
nonequilibrium systems such as those that have been used to model (among other things) …

Cells are the elementary units of living organisms, which are able to carry out many vital
functions. These functions rely on active processes on a microscopic scale. Therefore, they …

Unlike equilibrium statistical mechanics, with its well-established foundations, a similar
widely accepted framework for non-equilibrium statistical mechanics (NESM) remains …

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 …

We investigate the stationary distribution of asymmetric and weakly asymmetric simple
exclusion processes with open boundaries. We project the stationary distribution onto a …

We find the exact solution for the stationary state measure of the partially asymmetric
exclusion process on a ring with multiple species of particles. The solution is in the form of a …

We derive a matrix product formula for symmetric Macdonald polynomials. Our results are
obtained by constructing polynomial solutions of deformed Knizhnik–Zamolodchikov …

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 …

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

In this work we construct the stationary measure of the N species totally asymmetric simple
exclusion process in a matrix product formulation. We make the connection between the …