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) …

There has been considerable interest recently in the subject of patterns in permutations and
words, a new branch of combinatorics with its roots in the works of Rotem, Rogers, and …

We introduce the notion of crossings and nestings of a permutation. We compute the
generating function of permutations with a fixed number of weak exceedances, crossings …

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

We study mixing times of the symmetric and asymmetric simple exclusion process on the
segment where particles are allowed to enter and exit at the endpoints. We consider …

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 …

We show that the stationary measure for the totally asymmetric simple exclusion process on
a segment with open boundaries is given by a marginal of a two-line measure with a simple …

The stationary measures of the Kardar–Parisi–Zhang equation on an interval have been
computed recently. We present a rather direct derivation of this result by taking the weak …