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 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 Z<−L occupied by first class particles, all the sites of Z [−L,0] occupied by second class particles, and the rest of the sites of 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 Γ ⊂ 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 Γ.

Color-position symmetry in interacting particle systems

“…Note that this distribution significantly depends on q. Also note that this result contradicts [GSZ,Conjecture 1.2].…”