@article{EJP12,
author = {Janko Gravner},
title = {Percolation Times in Two-Dimensional Models For Excitable Media},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {1},
year = {1996},
keywords = {additive growth dynamics, excitable media, Greenberg--Hastings model, percolation.},
abstract = {The three-color Greenberg--Hastings model (GHM) is a simple cellular automaton model for an excitable medium. Each site on the lattice $Z^2$ is initially assigned one of the states 0, 1 or 2. At each tick of a discrete--time clock, the configuration changes according to the following synchronous rule: changes $1\to 2$ and $2\to 0$ are automatic, while an $x$ in state 0 may either stay in the same state or change to 1, the latter possibility occurring iff there is at least one representative of state 1 in the local neighborhood of $x$. Starting from a product measure with just 1's and 0's such dynamics quickly die out (turn into 0's), but not before 1's manage to form infinite connected sets. A very precise description of this ``transient percolation'' phenomenon can be obtained when the neighborhood of $x$ consists of 8 nearest points, the case first investigated by S. Fraser and R. Kapral. In addition, first percolation times for related monotone models are addressed.},
pages = {no. 12, 1-19},
issn = {1083-6489},
doi = {10.1214/EJP.v1-12},
url = {http://ejp.ejpecp.org/article/view/12}}