Related papers: Limit processes for TASEP with shocks and rarefact…
Consider the stationary measure of open asymmetric simple exclusion process (ASEP) on the lattice $\{1,\dots,n\}$. Taking $n$ to infinity while fixing the jump rates, this measure converges to a measure on the semi-infinite lattice. In the…
We consider the asymmetric simple exclusion process (ASEP) on the positive integers with an open boundary condition. We show that, when starting devoid of particles and for a certain boundary condition, the height function at the origin…
We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the…
We consider the asymmetric simple exclusion process on $\mathbb{Z}$ with a single second class particle initially at the origin. The first class particles form two rarefaction fans which come together at the origin, where the large time…
A quantitative central limit theorem for the simple symmetric exclusion process (SSEP) on a $d$-dimensional discrete torus is proven. The argument is based on a comparison of the generators of the density fluctuation field of the SSEP and…
In this paper, we study a two-lane totally asymmetric simple exclusion process (TASEP) coupled with random attachment and detachment of particles (Langmuir kinetics) in both lanes under open boundary conditions. Our model can describe the…
We introduce new integrable exclusion and zero-range processes on the one-dimensional lattice that generalize the $q$-Hahn TASEP and the $q$-Hahn Boson (zero-range) process introduced in [Pov13] and further studied in [Cor14], by allowing…
We explore the stationary densities and domain walls in the steady states of a pair of asymmetric exclusion processes (TASEP) antiparallelly coupled to two particle reservoirs without any spatial extent by using the model in Haldar et al.,…
We extend the paradigmatic and versatile TASEP (Totally Asymmetric Simple Exclusion Process) for stochastic 1d transport to allow for two different particle species, each having specific entry and exit rates. We offer a complete mean-field…
We obtain a new relation between the distributions $\mu_t$ at different times $t\ge 0$ of the continuous-time TASEP (Totally Asymmetric Simple Exclusion Process) started from the step initial configuration. Namely, we present a…
We consider the two-point function of the totally asymmetric simple exclusion process with stationary initial conditions. The two-point function can be expressed as the discrete Laplacian of the variance of the associated height function.…
We study a totally asymmetric simple exclusion process (TASEP) with one defect site, hopping rate $q<1$, near the system boundary. Regarding our system as a pair of uniform TASEP's coupled through the defect, we study various methods to…
We consider a $q$-TASEP model started from step initial condition where all but finitely many particles have speed $1$ and a few particles are slower. It is shown in [9] that the rescaled particles position of $q$-TASEP with identical…
We consider the asymmetric simple exclusion process (ASEP) with forward hopping rate 1, backward hopping rate q and periodic boundary conditions. We show that the Bethe equations of ASEP can be decoupled, at all order in perturbation in the…
We introduce a model of a totally asymmetric simple exclusion process (TASEP) on a tree network where the aggregate hopping rate is constant from level to level. With this choice for hopping rates the model shows the same phase diagram as…
We obtain two-sided bounds for the density of stochastic processes satisfying a weak H\"ormander condition. In particular we consider the cases when the support of the density is not the whole space and when the density has various…
We consider the asymmetric exclusion process (ASEP) in one dimension on sites $i = 1,..., N$, in contact at sites $i=1$ and $i=N$ with infinite particle reservoirs at densities $\rho_a$ and $\rho_b$. As $\rho_a$ and $\rho_b$ are varied, the…
We study the asymptotic speed of a second class particle in the two-species asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$ with each particle belonging either to the first class or the second class. For any fixed non-negative…
We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an…
We revisit the defect-induced nonequilibrium phase transition from a largely homogeneous free-flow phase to a phase-separated congested phase in the sublattice totally asymmetric simple exclusion process (TASEP) with local deterministic…