Coarsening with a frozen vertex

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

Research output: Contribution to journalArticlepeer-review

Abstract

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 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.

Original languageEnglish (US)
Article number9
JournalElectronic Communications in Probability
Volume21
DOIs
StatePublished - 2016

Keywords

  • Coarsening models
  • Frozen vertex
  • Zero-temperature glauber dynamics

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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