相关论文: KPZ statistics of second class particles in ASEP v…

We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate $p\in(1/2,1]$ and to the left at rate $1-p$, interacting by exclusion. In the initial state there is a finite region…

We consider the asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$. For continuous densities, ASEP is in local equilibrium for large times, at discontinuities however, one expects to see a dynamical phase transition, i.e. a mixture…

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…

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 consider the one-dimensional asymmetric zero-range process starting from a step decreasing profile. In the hydrodynamic limit this initial condition leads to the rarefaction fan of the associated hydrodynamic equation. Under this initial…

We consider any fixed $d\in\mathbb{Z}_{>0}$ number of second class particles in the asymmetric simple exclusion process (ASEP), constructed via a basic coupling of two ASEPs. We give the joint distribution of the positions of the second…

We consider the second class particle in half-line open TASEP under two different initial conditions with shock discontinuities. The exact formulas for the distribution of the second class particle can be derived by using the color-position…

We consider all totally asymmetric simple exclusion processes (TASEPs) whose transition probabilities are given in the Sch\"utz-type formulas and which jump with homogeneous rates. We show that the multi-point distribution of particle…

We identify the ballistically and diffusively rescaled limit distribution of the second class particle position in a wide range of asymmetric and symmetric interacting particle systems with established hydrodynamic behavior, respectively…

We consider the totally asymmetric simple exclusion process (TASEP) starting with a shock discontinuity at the origin, with asymptotic densities $\lambda$ to the left of the origin and $\rho$ to the right of it and $\lambda<\rho$. We find…

We consider the asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$ with initial data such that in the large time particle density $\rho(\cdot)$ a discontinuity (shock) at the origin is created. At the shock, the value of $\rho$…

We consider the TASEP on Z with two blocks of particles having different jump rates. We study the large time behavior of particles' positions. It depends both on the jump rates and the region we focus on, and we determine the complete…

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…

We consider the totally asymmetric simple exclusion process (TASEP) with two different initial conditions with shock discontinuities formed by blocks of fully packed particles. Initially a second class particle is at the left of a shock…

We prove a strong law of large numbers for the location of the second class particle in a totally asymmetric exclusion process when the process is started initially from a decreasing shock. This completes a study initiated in Ferrari and…

We consider the totally asymmetric simple exclusion process with initial conditions and/or jump rates such that shocks are generated. If the initial condition is deterministic, then the shock at time t will have a width of order t^{1/3}. We…

We discuss the approximate phenomenological description of the motion of a single second-class particle in a two-species totally asymmetric simple exclusion process (TASEP) on a 1D lattice. Initially, the second class particle is located at…

We consider the totally asymmetric simple exclusion process with \emph{soft-shock} initial particle density, which is a step function increasing in the direction of flow and the step size chosen small to admit KPZ scaling. The initial…

We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the…

In [AAV] Amir, Angel and Valk{\'o} studied a multi-type version of the totally asymmetric simple exclusion process (TASEP) and introduced the TASEP speed process, which allowed them to answer delicate questions about the joint distribution…