Limiting speed of a second class particle in ASEP

Abstract

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 integer $L$, we consider the two-species ASEP started from the initial data with all the sites of ${\mathbb{Z}}_{<-L}$ occupied by first class particles, all the sites of ${\mathbb{Z}}_{[-L,0]}$ occupied by second class particles, and the rest of the sites of $\mathbb{Z}$ unoccupied. With these initial conditions, we show that the speed of the leftmost second class particle converges weakly to a distribution supported on a symmetric compact interval $\Gamma \subset \mathbb{R}$. Furthermore, the limiting distribution is shown to have the same law as the minimum of $L+1$ independent random samples drawn uniformly from the interval $\Gamma$.

12 pages, 2 figures

References in corpus (2)

• Asymptotics in ASEP with Step Initial Condition
• The motion of a second class particle for the tasep starting from a decreasing shock profile