Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP

Abstract

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 Airy_1 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.

39 pages,6 figures

References in corpus (8)

• Fluctuation properties of the TASEP with periodic initial configuration
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Fluctuations of the one-dimensional polynuclear growth model with external sources
• Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
• Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
• Fluctuations of a one-dimensional polynuclear growth model in a half space
• Determinant solution for the Totally Asymmetric Exclusion Process with parallel update
• Polynuclear growth model, GOE${}^2$ and random matrix with deterministic source

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