Pfaffian Schur processes and last passage percolation in a half-quadrant
Abstract
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-dimensional crossover between the GUE, GOE and GSE distribution by studying the multipoint distribution of last passage times close to the diagonal when the size of the diagonal weights is simultaneously scaled close to the critical point. We expect that this crossover arises universally in KPZ growth models in half-space. Along the way, we introduce a method to deal with diverging correlation kernels of point processes where points collide in the scaling limit.
Keywords
Cite
@article{arxiv.1606.00525,
title = {Pfaffian Schur processes and last passage percolation in a half-quadrant},
author = {Jinho Baik and Guillaume Barraquand and Ivan Corwin and Toufic Suidan},
journal= {arXiv preprint arXiv:1606.00525},
year = {2024}
}
Comments
v5: this version corrects mistakes in the definition of the crossover kernel in Section 2.5. v4: minor typos corrected. v3: 58 pages, to appear in Annals of Probability. The initial submission arXiv:1606.00525v1 has been splitted in two parts. This paper contains only the results on last passage percolation. The results on the facilitated TASEP appear in arXiv:1707.01923