Under typical scaling, the last passage time field of the directed last passage percolation model with exponential site distributions converges to the KPZ fixed point. In this talk, we consider an atypical scenario in which the last passage time to a specific site is unusually large and explore how the last passage time field changes under this one-point upper large deviation event. We study a conditional law of large numbers and compute the limiting fluctuations in certain regimes. Our proofs rely on an analysis of explicit multi-point distributions. This talk is based on joint work with Jinho Baik and Dylan Cordaro.

Recent years have seen significant progress in understanding fluctuations in half-space models within the KPZ universality class. In this talk I will discuss a Pfaffian Schur process, which is a measure on a sequence of partitions, which was introduced by Borodin and Rains as a Pfaffian analog of the determinantal Schur processes introduced by Okounkov and Reshetikhin. The model we investigate arises in a half-quadrant last passage percolation model, which has i.i.d. geometric weights with parameter $\alpha \in (0,1)$ off of the main diagonal and with parameter $c \in (0, \alpha^{-1})$ on the main diagonal. We show that when $c$ is subcritical the line ensembles formed by the parts of our random partitions converge uniformly over compact sets to the Airy line ensemble; when $c$ is critically scaled with the size of the system the ensemble instead converges to the Airy wanderer line ensemble with a single parameter; and when $c$ is supercritical we will see both Gaussian and Airy line ensemble in the limit.