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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 50 open journal systems 


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

Alexei Borodin, Caltech
Patrik L Ferrari, WIAS Berlin


Abstract
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 Airy1 and Airy2 processes. This includes fluctuations of the height profile for a fixed time and fluctuations of a tagged particle's trajectory as special cases.


Full text: PDF

Pages: 1380-1418

Published on: August 25, 2008


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Electronic Journal of Probability. ISSN: 1083-6489