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November 2018 Pfaffian Schur processes and last passage percolation in a half-quadrant
Jinho Baik, Guillaume Barraquand, Ivan Corwin, Toufic Suidan
Ann. Probab. 46(6): 3015-3089 (November 2018). DOI: 10.1214/17-AOP1226

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.

Citation

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Jinho Baik. Guillaume Barraquand. Ivan Corwin. Toufic Suidan. "Pfaffian Schur processes and last passage percolation in a half-quadrant." Ann. Probab. 46 (6) 3015 - 3089, November 2018. https://doi.org/10.1214/17-AOP1226

Information

Received: 1 July 2016; Revised: 1 August 2017; Published: November 2018
First available in Project Euclid: 25 September 2018

zbMATH: 06975483
MathSciNet: MR3857852
Digital Object Identifier: 10.1214/17-AOP1226

Subjects:
Primary: 60K35, 82C23
Secondary: 05E05, 60B20, 60G55

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 6 • November 2018
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