Coarsening with a frozen vertex

Michael Damron, Hana Kogan, Charles M. Newman, Vladas Sidoravicius
2016 Electronic Communications in Probability  
In the standard nearest-neighbor coarsening model with state space {−1, +1} Z 2 and initial state chosen from symmetric product measure, it is known (see [2] ) 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.
doi:10.1214/16-ecp4785 fatcat:mvss6322uzdnbcuv2l4blm6tja