Percolation times in Two{dimensional Models for Excitable Media Percolation times in Two{dimensional Models for Excitable Media

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 connguration changes according to the following synchronous rule: changes 1 ! 2 and 2 ! 0 are automatic, while an x in state 0 may either stay in the same state or change to 1, the latter possibility occurring ii 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 innnite 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 rst investigated by S. Fraser and R. Kapral. In addition, rst percolation times for related monotone models are addressed.