Abstract
Gibbs measures are studied using a Markov chain on the nonnegative integers. Uniqueness of Gibbs measures follows from absorption of the chain at $\{0\}$. To this end, we derive a certain inequality. For one-dimensional systems this extends a well-known uniqueness result of Ruelle and for models near the $1/r^2$-interaction Ising model it is a natural improvement of some other results.
Citation
Henry Berbee. "Uniqueness of Gibbs Measures and Absorption Probabilities." Ann. Probab. 17 (4) 1416 - 1431, October, 1989. https://doi.org/10.1214/aop/1176991162
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