# Large time asymptotics of growth models on space-like paths I: PushASEP

@article{Borodin2007LargeTA, title={Large time asymptotics of growth models on space-like paths I: PushASEP}, author={Alexei Borodin and Patrik L. Ferrari Caltech and Wias Berlin}, journal={Electronic Journal of Probability}, year={2007}, volume={13}, pages={1380-1418} }

We consider a new interacting particle system on the one-dimensional lattice that interpolates between TASEP and Toom's model: A particle cannot jump to the right if the neighboring site is occupied, and when jumping to the left it simply pushes all the neighbors that block its way. We prove that for flat and step initial conditions, the large time fluctuations of theheight function of the associated growth model along any space-like path are described by the Airy 1 and Airy 2 processes. This…

## 146 Citations

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Abstract
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The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in the TASEP with the step initial condition.…

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Dynamical properties of a tagged particle in the totally asymmetric simple exclusion process with the step-type initial condition Abstract The one-dimensional totally asymmetric simple exclusion…