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Föllmer, H.: On entropy and information gain in random fields. Z. Wahrscheinlichkeitstheorie verw. Gebiete 26, 207–217 (1973)
Föllmer, H.: Phase transition and Martin boundary. In Sém. de Prob. IX, Lecture Notes in Mathematics 465, 305–318. Berlin-Heidelberg-New York: Springer 1975
Künsch, H.: Gaussian Markov random fields. J. Fac. Sci. Univ. Tokyo Sec. IA Math. 26, 53–73 (1979)
Lanford, III O.E., Ruelle, D.: Observables at infinity and states with short range correlations in statistical mechanics. Comm. Math. Phys. 13, 194–215 (1969)
Lebowitz, J.L., Presutti, E.: Statistical mechanics of systems of unbounded spins. Comm. Math. Phys. 50, 195–218 (1976)
Nguyen, X.X., Zessin, H.: Ergodic theorems for spatial processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 48, 133–158 (1979)
Pirlot, M.: A strong variational principle for continuous spin systems. J. Appl. Probability 17, 47–58 (1980)
Preston, C.: Random fields. Lecture Notes in Mathematics 534. Berlin-Heidelberg-New York: Springer 1976
Preston, C.: A note on conditions under which Lemma 7.2 of Preston. Random fields, can be obtained. Private communication (1979)
Rosanov, Yu.A.: On Gaussian fields with given conditional distributions. Theory Probability Appl. 12, 381–391 (1967)
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)
Spitzer, F.: Champs de Markov Gaussiens. Ecole d'été de prob. Saint Flour III, Lecture Notes in Mathematics 390, 179–185. Berlin-Heidelberg-New York: Springer 1974
Tempel'man, A.A.: Ergodic theorems for general dynamical systems. Transactions Moscow Math. Soc. 26, 94–132 (1972)
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Künsch, H. Almost sure entropy and the variational principle for random fields with unbounded state space. Z. Wahrscheinlichkeitstheorie verw Gebiete 58, 69–85 (1981). https://doi.org/10.1007/BF00536196
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DOI: https://doi.org/10.1007/BF00536196