A simple proof of the stability criterion of Gray and Griffeath
type: Item
instance of: scholarly article
title: A simple proof of the stability criterion of Gray and Griffeath
zbMATH Open document ID: 0639.60094
DOI: 10.1007/BF00356107
author: Maury Bramson
author: Rick Durrett
publication date: 1988-01-01T00:00:00Z
review text: \textit{L. Gray} and \textit{D. Griffeath} [Ann. Probab. 10, 67-85 (1982; Zbl 0483.60090)] studied attractive nearest neighbor spin systems on the integers having ``all 0's'' and ``all 1's'' as traps. Using the contour methods, 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.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 4043009
zbMATH Keywords: attractive nearest neighbor spin systems
zbMATH Keywords: contour method
zbMATH Keywords: renormalized site construction
Wikidata QID: Q105583345
MaRDI profile type: Publication
cites work: Oriented percolation in two dimensions
cites work: A stability criterion for attractive nearest neighbor spin systems on Z
cites work: Q5185817
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 4043009