Electronic Journal of Probability

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

Alexei Borodin and Patrik Ferrari

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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<sub>1</sub> and Airy<sub>2</sub> processes. This includes fluctuations of the height profile for a fixed time and fluctuations of a tagged particle's trajectory as special cases.

Article information

Electron. J. Probab., Volume 13 (2008), paper no. 50, 1380-1418.

Accepted: 25 August 2008
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 82C22: Interacting particle systems [See also 60K35]
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 15A52

stochastic growth KPZ determinantal processes Airy processes

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Borodin, Alexei; Ferrari, Patrik. Large time asymptotics of growth models on space-like paths I: PushASEP. Electron. J. Probab. 13 (2008), paper no. 50, 1380--1418. doi:10.1214/EJP.v13-541. https://projecteuclid.org/euclid.ejp/1464819123

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