Pfaffian Schur processes and last passage percolation in a half-quadrant
From MaRDI portal
Publication:1621437
DOI10.1214/17-AOP1226zbMATH Open1428.60134arXiv1606.00525WikidataQ129194810 ScholiaQ129194810MaRDI QIDQ1621437
Author name not available (Why is that?)
Publication date: 8 November 2018
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1606.00525
No records found.
No records found.
This page was built for publication: Pfaffian Schur processes and last passage percolation in a half-quadrant
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1621437)
