The Annals of Probability

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

Jinho Baik, Guillaume Barraquand, Ivan Corwin, and Toufic Suidan

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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
Received: July 2016
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

Subjects
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)

Keywords
Last passage percolation KPZ universality class Tracy–Widom distributions Schur process Fredholm Pfaffian phase transition

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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