  We continue the investigation of limit fluctuations of stationary measures of
the asymmetric simple exclusion processes with open boundaries (open ASEP),
complementing the recent result by Bryc et al. (2023). It was shown therein
that in the fan region of the phase diagram, an appropriate scaling limit of
the height function of open ASEP converges in distribution to a stochastic
process introduced by Barraquand and Le Doussal (2022), known as the stationary
measure of the (conjectural) open KPZ fixed point. In this paper, we establish
the corresponding convergence in the shock region. Our proof is based on the
integral representation of the matrix product ansatz in terms of Askey-Wilson
signed measures introduced by Wang et al. (2023). The analysis of the
asymptotic behavior is more delicate here than in the fan region. In
particular, our proof of the duality formula for the stationary measures of the
open KPZ fixed point in the shock region is different from the approach by Bryc
et al. (2023) taken in the fan region: ours relies crucially on a recent result
by Bryc and Zatitskii (2024).
