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arXiv · 1512.08491

Coarsening with a frozen vertex

M. Damron·H. Kogan·C. M. Newman·V. Sidoravicius
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Abstract

In the standard nearest-neighbor coarsening model with state space $\{-1,+1\}^{\mathbb{Z}^2}$ and initial state chosen from symmetric product measure, it is known (see~\cite{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.

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M. Damron, H. Kogan, C. M. Newman, V. Sidoravicius. 2015-12-28. Coarsening with a frozen vertex. https://arxiv.org/abs/1512.08491

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