Electronic Journal of Probability

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

Alexei Borodin and Patrik Ferrari

Full-text: Open access

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 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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819123

Digital Object Identifier
doi:10.1214/EJP.v13-541

Mathematical Reviews number (MathSciNet)
MR2438811

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

Keywords
stochastic growth KPZ determinantal processes Airy processes

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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