Open Access
2016 Coarsening with a frozen vertex
Michael Damron, Hana Kogan, Charles M. Newman, Vladas Sidoravicius
Electron. Commun. Probab. 21: 1-4 (2016). DOI: 10.1214/16-ECP4785


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 [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.


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Michael Damron. Hana Kogan. Charles M. Newman. Vladas Sidoravicius. "Coarsening with a frozen vertex." Electron. Commun. Probab. 21 1 - 4, 2016.


Received: 29 December 2015; Accepted: 26 January 2016; Published: 2016
First available in Project Euclid: 15 February 2016

zbMATH: 1336.60186
MathSciNet: MR3485378
Digital Object Identifier: 10.1214/16-ECP4785

Primary: 60K35 , 82C22

Keywords: coarsening models , frozen vertex , zero-temperature Glauber dynamics

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