Uniqueness of Gibbs Measures and Absorption Probabilities
Berbee, Henry
Ann. Probab., Tome 17 (1989) no. 4, p. 1416-1431 / Harvested from Project Euclid
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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.
Publié le : 1989-10-14
Classification:  Uniqueness of Gibbs measures,  positive operator,  Markov operator,  duality,  absorbing state,  inequality,  Perron-Frobenius theorem,  82A25,  47D45,  60K35 
@article{1176991162,
     author = {Berbee, Henry},
     title = {Uniqueness of Gibbs Measures and Absorption Probabilities},
     journal = {Ann. Probab.},
     volume = {17},
     number = {4},
     year = {1989},
     pages = { 1416-1431},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991162}
}

Berbee, Henry. Uniqueness of Gibbs Measures and Absorption Probabilities. Ann. Probab., Tome 17 (1989) no. 4, pp.  1416-1431. http://gdmltest.u-ga.fr/item/1176991162/