A sufficient condition for non-coexistence of one dimensional multicolor contact processes (Q1335387)

The authors study a Markov process, whose state space consists of the configurations on \(\mathbb{Z}\), where each site is occupied by grass, bushes or trees with corresponding transition rates. They prove non-existence of bushes and trees as time \(t \to \infty\) for large birth rates of trees using oriented percolation. The stronger result, that in this case bushes die out, was already obtained by \textit{R. Durrett} and \textit{G. Swindle} [Stochastic Processes Appl. 37, No. 1, 19-31 (1991; Zbl 0722.60106)].