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

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

2007-07-28

arxiv.org/abs/0707.4207v1

Comm. Math. Phys. 283 (2008) 417-449

Physics

Mathematical Physics

39 pages,6 figures

Scientific paper

10.1007/s00220-008-0515-4

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.

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