2007/07/28 by Alexei Borodin, Patrik L. Ferrari, Tomohiro Sasamoto · 3 citations
Mathematics · Physics and Astronomy · #Asymmetric simple exclusion process #Classical mechanics #Combinatorics #Computer science #Dimension (graph theory) #Geometry #Limit (mathematics) #Mathematical analysis #Mathematics #Moment (physics) #Path (computing) #Physics #Plane (geometry) #Random Matrices and Applications #Scaling #Scaling limit #Second moment of area #Space (punctuation) #Space time #Statistics #Stochastic processes and statistical mechanics #Surface (topology) #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #math.PR #msc:15A52 #msc:60K35 #msc:82C22
paper · pdf · doi:10.1007/s00220-008-0515-4
published as Comm. Math. Phys. 283 (2008) 417-449 · 39 pages,6 figures
arxiv created 2007/07/28 · openalex publication_date 2008/05/28 · arxiv updated 2010/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a signed determinantal point process. The long time scaling limit of the surface height is shown to coincide with the Airy1 process. This result holds more generally for the observation points located along any space-like path in the space-time plane. We also obtain the corresponding results for the discrete time TASEP (totally asymmetric simple exclusion process) with parallel update.