@article{EJP598,
author = {Gregor Sega},
title = {Large-range constant threshold growth model in one dimension},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {14},
year = {2009},
keywords = {growth model; asymptotic propagation velocity; invariant distribution},
abstract = {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 $n^2/2v$.},
pages = {no. 6, 119-138},
issn = {1083-6489},
doi = {10.1214/EJP.v14-598},
url = {http://ejp.ejpecp.org/article/view/598}}