The Annals of Probability
- Ann. Probab.
- Volume 46, Number 6 (2018), 3015-3089.
Pfaffian Schur processes and last passage percolation in a half-quadrant
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.
Ann. Probab., Volume 46, Number 6 (2018), 3015-3089.
Received: July 2016
Revised: August 2017
First available in Project Euclid: 25 September 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C23: Exactly solvable dynamic models [See also 37K60]
Secondary: 60G55: Point processes 05E05: Symmetric functions and generalizations 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
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