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

with Alexei Borodin and Tomohiro Sasamoto.

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.

Postscript file: [PS]

PDF file: [PDF]

arXiv: 0707.4207