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

Borodin, Alexei and Ferrari, Patrik L. (2008) Large time asymptotics of growth models on space-like paths I: PushASEP. Electronic Journal of Probability, 13 (50). pp. 1380-1418. ISSN 1083-6489. https://resolver.caltech.edu/CaltechAUTHORS:BORejp08

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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 the height 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://www.math.washington.edu/~ejpecp/viewarticle.php?id=1839&layout=abstractPublisherUNSPECIFIED
Additional Information:Copyright © 2008, The Authors. Submitted to EJP on August 30, 2007, final version accepted August 11, 2008. are very grateful to the anonymous referee for careful reading and a number of constructive remarks. A. Borodin was partially supported by the NSF grants DMS-0402047 and DMS-0707163.
Funders:
Funding AgencyGrant Number
National Science FoundationDMS-0402047
National Science FoundationDMS-0707163
Subject Keywords:stochastic growth, KPZ, determinantal processes, Airy processes
Issue or Number:50
Record Number:CaltechAUTHORS:BORejp08
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:BORejp08
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11810
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:01 Oct 2008 06:39
Last Modified:03 Oct 2019 00:22

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