The half-space Airy stat process

We study the multipoint distribution of stationary half-space last passage percolation with exponentially weighted times. We derive both finite-size and asymptotic results for this distribution. In the latter case we observe a new one-parameter process we call half-space Airy stat. It is a one-parameter generalization of the Airy stat process of Baik-Ferrari-P\'ech\'e, which is recovered far away from the diagonal. All these results extend the one-point results previously proven by the authors.