The pinned half-space Airy line ensemble

Abstract

Half-space models in the Kardar-Parisi-Zhang (KPZ) universality class exhibit rich boundary phenomena that alter the asymptotic behavior familiar from their full-space counterparts. A distinguishing feature of these systems is the presence of a boundary parameter that governs a transition between subcritical, critical, and supercritical regimes, characterized by different scaling exponents and fluctuation statistics. In this paper we construct the pinned half-space Airy line ensemble $\mathcal{A}^{\mathrm{hs}; \infty}$ on $[0,\infty)$ -- a natural half-space analogue of the Airy line ensemble -- expected to arise as the universal scaling limit of supercritical half-space KPZ models. The ensemble $\mathcal{A}^{\mathrm{hs}; \infty}$ is obtained as the weak limit of the critical half-space Airy line ensembles $\mathcal{A}^{\mathrm{hs}; \varpi}$ introduced in arXiv:2505.01798 as the boundary parameter $\varpi$ tends to infinity. We show that $\mathcal{A}^{\mathrm{hs}; \infty}$ has a Pfaffian point process structure with an explicit correlation kernel and that, after a parabolic shift, it satisfies a one-sided Brownian Gibbs property described by pairwise pinned Brownian motions. Far from the origin, $\mathcal{A}^{\mathrm{hs}; \infty}$ converges to the standard Airy line ensemble, while at the origin its distribution coincides with that of the ordered eigenvalues (with doubled multiplicity) of the stochastic Airy operator with $\beta = 4$.