Electronic Communications in Probability

Coarsening with a frozen vertex

Michael Damron, Hana Kogan, Charles M. Newman, and Vladas Sidoravicius

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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.

Article information

Electron. Commun. Probab., Volume 21 (2016), paper no. 9, 4 pp.

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

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35]

coarsening models zero-temperature Glauber dynamics frozen vertex

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Damron, Michael; Kogan, Hana; Newman, Charles M.; Sidoravicius, Vladas. Coarsening with a frozen vertex. Electron. Commun. Probab. 21 (2016), paper no. 9, 4 pp. doi:10.1214/16-ECP4785. https://projecteuclid.org/euclid.ecp/1455560033

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