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References
Benfatto, G., Presutti, E., Pulvirenti, M.: DLR measures for one-dimensional harmonic systems, Z. Wahrscheinlichkeitstheorie und verw. Gebiete 41, 305–312 (1978).
Cassandro, M., Olivieri, E., Pellegrinotti, A., Presutti, E.: Existence and uniqueness of DLR measures for unbounded spin systems, Z. Wahrscheinlichkeitstheorie und verw. Gebiete 41, 313–334 (1978).
De Masi, M.: One-dimensional DLR invariant measures are regular, Comm. Math. Phys. 67, 43–50 (1979).
Dobrushin, R.L.: The description of a random field by means of conditional probabilities and conditions of its regularity (in Russian), Teor. Verojatnost. i Primenen. 13, 201–229 (1968). (English transl.: Theor. Probability Appl. 13, 197–224 (1968)).
Dobrushin, R.L.: Prescribing a system of random variables by conditional distributions (in Russian), Teor. Verojatnost. i Premenen. 15, 469–497 (1970). (English transl.: Theor. Probability Appl. 15, 458–486 (1970)).
Kesten, H.: Existence and uniqueness of countable one-dimensional Markov random fields, Ann. Probability 4, 557–569 (1976).
Lebowitz, J.L., Presutti, E.: Statistical mechanics of systems of unbounded spins, Comm. Math. Phys. 50, 195–218 (1976). Erratum: ibid. 78, 151 (1980).
Papangelou, F.: Stationary one-dimensional Markov random fields with a continuous state space. In “Probability, Statistics and Analysis” (ed. J.F.C. Kingman and G.E.H. Reuter), London Math. Soc. Lecture Note Series 79, 199–218. Cambridge: Cambridge University Press 1983.
Papangelou, F.: On the absence of phase transition in one-dimensional random fields. (I) Sufficient conditions. Submitted.
Papangelou, F.: On the absence of phase transition in one-dimensional random fields. (II) Superstable spin systems. Submitted.
Ruelle, D.: Superstable interactions in classical statistical mechanics, Comm. Math. Phys. 18, 127–159 (1970).
Ruelle, D.: Probability estimates for continuous spin systems, Comm. Math. Phys. 50, 189–194 (1976).
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Papangelou, F. (1984). The uniqueness of regular DLR measures for certain one-dimensional spin systems. In: Truman, A., Williams, D. (eds) Stochastic Analysis and Applications. Lecture Notes in Mathematics, vol 1095. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099120
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DOI: https://doi.org/10.1007/BFb0099120
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