A simple proof of the stability criterion of Gray and Griffeath

Maury Bramson, Rick Durrett

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


Gray and Griffeath studied attractive nearest neighbor spin systems on the integers having "all 0's" and "all 1's" as traps. Using the contour method, they established a necessary and sufficient condition for the stability of the "all 1's" equilibrium under small perturbations. In this paper we use a renormalized site construction to give a much simpler proof. Our new approach can be used in many situations as a substitute for the contour method.

Original languageEnglish (US)
Pages (from-to)293-298
Number of pages6
JournalProbability Theory and Related Fields
Issue number2
StatePublished - Dec 1988


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