• Corpus ID: 85459288

Limiting speed of a second class particle in ASEP

@article{Ghosal2019LimitingSO,
  title={Limiting speed of a second class particle in ASEP},
  author={Promit Ghosal and Axel Saenz and Ethan C. Zell},
  journal={arXiv: Probability},
  year={2019}
}

• Promit Ghosal, A. Saenz, Ethan C. Zell
• Published 22 March 2019
• Mathematics
• arXiv: Probability

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 $\Gamma$.