LA Probability Forum

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, and 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.