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Large Time Asymptotics of Growth Models on Space-like Paths II: PNG and Parallel TASEP

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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 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.

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Authors and Affiliations

  1. California Institute of Technology, Mathematics 253–37, Pasadena, CA, 91125, USA

    Alexei Borodin

  2. Weierstrass Institute (WIAS), Mohrenstr. 39, 10117, Berlin, Germany

    Patrik L. Ferrari

  3. Dept. of Mathematics and Informatics, Chiba University, 1-33 Yagot-cho, Inage, Chiba, 263-8522, Japan

    Tomohiro Sasamoto

Authors
  1. Alexei Borodin
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  2. Patrik L. Ferrari
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  3. Tomohiro Sasamoto
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Correspondence to Tomohiro Sasamoto.

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Communicated by H. Spohn

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Borodin, A., Ferrari, P.L. & Sasamoto, T. Large Time Asymptotics of Growth Models on Space-like Paths II: PNG and Parallel TASEP. Commun. Math. Phys. 283, 417–449 (2008). https://doi.org/10.1007/s00220-008-0515-4

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  • DOI: https://doi.org/10.1007/s00220-008-0515-4

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