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We consider the asymmetric simple exclusion process on $\mathbb{Z}$ with asingle second class particle initially at the origin. The first class particlesform two rarefaction fans which come together at the origin, where the largetime density jumps from $0$ to $1$. We are interested in $X(t)$, the positionof the second class particle at time $t$. We show that, under the KPZ $1/3$scaling, $X(t)$ is asymptotically distributed as the difference of twoindependent, $\mathrm{GUE}$-distributed random variables.The key part of theproof is to show that $X(t)$ equals, up to a negligible term, the difference ofa random number of holes and particles, with the randomness built up by ASEPitself. This provides a KPZ analogue to the 1994 result of Ferrari and Fontes\cite{FF94b}, where this randomness comes from the initial data and leads toGaussian limit laws.

KPZ statistics of second class particles in ASEP via mixing