Open Access
2009 Large-range constant threshold growth model in one dimension
Gregor Sega
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Electron. J. Probab. 14: 119-138 (2009). DOI: 10.1214/EJP.v14-598


We study a one dimensional constant threshold model in continuous time. Its dynamics have two parameters, the range $n$ and the threshold $v$. An unoccupied site $x$ becomes occupied at rate 1 as soon as there are at least $v$ occupied sites in $[x-n, x+n]$. As n goes to infinity and $v$ is kept fixed, the dynamics can be approximated by a continuous space version, which has an explicit invariant measure at the front. This allows us to prove that the speed of propagation is asymptoticaly $n^2/2v$.


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Gregor Sega. "Large-range constant threshold growth model in one dimension." Electron. J. Probab. 14 119 - 138, 2009.


Accepted: 27 January 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1189.60185
MathSciNet: MR2471662
Digital Object Identifier: 10.1214/EJP.v14-598

Primary: 60K35
Secondary: 82B23 , 82C22

Keywords: asymptotic propagation velocity , Growth model , Invariant distribution

Vol.14 • 2009
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