Coarsening with a frozen vertex

Original · EN

In the standard nearest-neighbor coarsening model with state space {-1,+1}ᶻ² and initial state chosen from symmetric product measure, it is known (see NNS) that almost surely, every vertex flips infinitely often. In this paper, we study the modified model in which a single vertex is frozen to +1 for all time, and show that every other site still flips infinitely often. The proof combines stochastic domination (attractivity) and influence propagation arguments.