2004/02/29 by Patrik L. Ferrari · 4 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Random Matrices and Applications #Stochastic processes and statistical mechanics #cond-mat.stat-mech #math-ph #math.MP #math.PR
paper · pdf · doi:10.1007/s00220-004-1204-6
published as Comm. Math. Phys., 252 (2004), 77-109 · 40 pages, 6 figures, LaTeX; Section 4 is substantially modified
arxiv created 2004/06/17 · openalex publication_date 2004/10/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. Through the Robinson-Schensted-Knuth (RSK) construction, one obtains the multilayer PNG model, which consists of a stack of non-intersecting lines, the top one being the PNG height. The statistics of the lines is translation invariant and at a fixed position the lines define a point process. We prove that for large times the edge of this point process, suitably scaled, has a limit. This limit is a Pfaffian point process and identical to the one obtained from the edge scaling of Gaussian orthogonal ensemble (GOE) of random matrices. Our results give further insight to the universality structure within the KPZ class of 1+1 dimensional growth models.