Related papers: Blocks in ASEP with step-Bernoulli initial conditi…
We consider an exclusion process on a periodic one-dimensional lattice where all particles perform simple symmetric exclusion at rate $1$ except for a single tracer particle, which performs partially simple asymmetric exclusion with rate…
We give an exact expression for the distribution of the position X(t) of a single second class particle in the asymmetric simple exclusion process (ASEP) where initially the second class particle is located at the origin and the first class…
In this paper, we consider zero range process with an initial condition which is equivalent to step initial condition in total asymmetric simple exclusion process (TASEP) as described in a paper by R\'akos, A. and Sch\"utz by using…
The one-dimensional asymmetric simple exclusion process (ASEP), where $N$ hard-core particles hop forward with rate $1$ and backward with rate $q<1$, is considered on a periodic lattice of $L$ site. Using KPZ universality and previous…
In this paper we analyze the steady state of the Asymmetric Simple Exclusion process with open boundaries and second class particles by deforming it through the introduction of spectral parameters. The (unnormalized) probabilities of the…
We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density $\rho$ on $\mathbb{Z}_-$ and $\lambda$ on $\mathbb{Z}_+$, and a second class particle initially at the origin. For…
The totally asymmetric simple exclusion process (TASEP) on the one-dimensional lattice with the Bernoulli \rho measure as initial conditions, 0<\rho<1, is stationary in space and time. Let N_t(j) be the number of particles which have…
We describe the translation invariant stationary states of the one dimensional discrete-time facilitated totally asymmetric simple exclusion process (F-TASEP). In this system a particle at site $j$ in $Z$ jumps, at integer times, to site…
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 investigate a balance network of the asymmetric simple exclusion process (ASEP). Subsystems consisting of ASEPs are connected by bidirectional links with each other, which results in balance between every pair of subsystems. The network…
We consider the $q$-totally asymmetric simple exclusion process ($q$-TASEP) in the stationary regime and study the fluctuation of the position of a particle. We first observe that the problem can be studied as a limiting case of an…
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…
Sampling from a random discrete distribution induced by a `stick-breaking' process is considered. Under a moment condition, it is shown that the asymptotics of the sequence of occupancy numbers, and of the small-parts counts (singletons,…
We consider a totally asymmetric simple exclusion on $\mathbb{Z}$ with the step initial condition, under the additional restriction that the first particle cannot cross a deterministally moving wall. We prove that such a wall may induce…
We investigate the asymmetric simple exclusion process (ASEP) on an interval with open boundaries. We provide a representation for its stationary distribution as a marginal of the top layer of a two-layer ensemble under Liggett's condition.…
We study the totally asymmetric simple exclusion process (TASEP) on $\mathbb{Z}$ with step initial condition, in which all particles have distinct types. Our main object of interest is the type of the rightmost particle -- the leader -- at…
In this paper we obtain general integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice with nearest neighbor hopping rates p to the right and q=1-p to the left. For the most part we…
By a geometrical treatment of the Bethe ansatz, we obtain an exact solution for the totally asymmetric exclusion process on a ring. We derive an explicit determinant expression for the non-stationary conditional probability…
We consider the totally asymmetric exclusion process on a ring in discrete time with the backward-ordered sequential update and particle-dependent hopping probabilities. Using a combinatorial treatment of the Bethe ansatz, we derive the…
We consider the stationary measure of the open asymmetric simple exclusion process (ASEP) with light particles. We prove several results on the asymptotic locations of the light particles under the stationary measure. Moreover, in the fan…