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In this talk I will present our work on the free boundary Schur process, which is a generalization of the original Schur process of Okounkov and Reshetikhin. This model after some shift-mixing is a Pfaffian process. I will introduce combinatorial random corner growth/LPP models corresponding to the free boundary Schur process and present some asymptotic results. The limiting behavior for these models is given by some new deformations of universal distributions of Schur processes. This is a joint work with D. Betea, J. Bouttier, and P. Nejjar.