We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p is an element of (1/2, 1.] and to the left at rate 1 - p, interacting by exclusion. In the initial ...

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 matrix product formulation and the queueing ...

The convergence of the totally asymmetric simple exclusion process to the solution of the Burgers equation is a classical result. In his seminal 1981 paper, Herman Rost proved the convergence of the density fields and local ...

A two-dimensional constrained diffusion model is presented and characterized by numerical simulations. The model generalizes the one-dimensional single-file diffusion model by considering a cage diffusion constraint induced ...

We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic ...

We consider the time evolution of an exactly solvable cellular automaton with random initial conditions both in the large-scale hydrodynamic limit and on the microscopic level. This model is a version of the totally ...

An explicit Fredholm determinant formula is derived for the multipoint distribution of the height function of the totally asymmetric simple exclusion process (TASEP) with arbitrary right-finite initial condition. The ...

We study a continuous-space version of the totally asymmetric simple exclusion process (TASEP), consisting of interacting Brownian particles subject to a driving force in a periodic external potential. In the one-dimensional ...

We study a continuous-space version of the totally asymmetric simple exclusion process (TASEP), consisting of interacting Brownian particles subject to a driving force in a periodic external potential. In the one-dimensional ...