Pfaffian Schur processes and last passage percolation in a half-quadrant

@article{Baik2018PfaffianSP,
  title={Pfaffian Schur processes and last passage percolation in a half-quadrant},
  author={Jinho Baik and Guillaume Barraquand and Ivan Corwin and Toufic M. Suidan},
  journal={The Annals of Probability},
  year={2018}
}
We study last passage percolation in a half-quadrant, which we analyze within the framework of Pfaffian Schur processes. For the model with exponential weights, we prove that the fluctuations of the last passage time to a point on the diagonal are either GSE Tracy-Widom distributed, GOE Tracy-Widom distributed, or Gaussian, depending on the size of weights along the diagonal. Away from the diagonal, the fluctuations of passage times follow the GUE Tracy-Widom distribution. We also obtain a two… 

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