test A phase transition for the contact process with avoidance on Z, Zn, and the star graph
This model presents a challenge because, unlike the classical contact process (α=0,) it has not been shown to be an attractive particle system. We study the survival dynamics of this model on the nearest-neighbor lattice Z, the cycle Zn, and the star graph. On Z, we show there is a phase transition in λ between almost sure extinction and positive probability of survival. On Zn, we show that as the number of vertices n→∞, there is a phase transition between log and exponential survival time in the size of the graph. On the star graph, we show that as n→∞ the survival time is polynomial in n for all values of λ and α. This contrasts with the classical contact process where the the survival time on the star graph is exponential in n for all values of λ.