## The Annals of Probability

### 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.

#### Article information

Source
Ann. Probab., Volume 46, Number 6 (2018), 3015-3089.

Dates
Revised: August 2017
First available in Project Euclid: 25 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.aop/1537862428

Digital Object Identifier
doi:10.1214/17-AOP1226

Mathematical Reviews number (MathSciNet)
MR3857852

Zentralblatt MATH identifier
06975483

#### Citation

Baik, Jinho; Barraquand, Guillaume; Corwin, Ivan; Suidan, Toufic. Pfaffian Schur processes and last passage percolation in a half-quadrant. Ann. Probab. 46 (2018), no. 6, 3015--3089. doi:10.1214/17-AOP1226. https://projecteuclid.org/euclid.aop/1537862428

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