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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 6 open journal systems 


Large-range constant threshold growth model in one dimension

Gregor Sega, Faculty of Mathematics and Physics, University of Ljubljana


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 n2/2v.


Full text: PDF

Pages: 119-138

Published on: January 27, 2009
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Electronic Journal of Probability. ISSN: 1083-6489