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On the Ergodic Properties of Gibbs States for Attractive Specifications
Author(s) -
Hulse Paul
Publication year - 1991
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-43.1.119
Subject(s) - ergodic theory , bernoulli's principle , gibbs state , invariant (physics) , lattice (music) , gibbs sampling , statistical physics , translation (biology) , mathematics , physics , pure mathematics , thermodynamics , mathematical physics , quantum mechanics , statistics , chemistry , quantum , bayesian probability , biochemistry , messenger rna , gene , acoustics
We consider Gibbs states for attractive specifications on a one‐dimensional lattice. If the specification is translation‐invariant, there exist ergodic, translation‐invariant Gibbs states v + and v − with the property that there is a unique Gibbs state if and only if v + = v − . We show that v + and v − are Bernoulli measures for the shift.