Dobrushin, R. L.; Tirozzi, Brunello The central limit theorem and the problem of equivalence of ensembles. (English) Zbl 0391.60095 Commun. Math. Phys. 54, 173-192 (1977). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 33 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60F05 Central limit and other weak theorems Keywords:Markov Fields; Canonical Ensemble; GibBs Ensemble; Central Limit Theorem PDF BibTeX XML Cite \textit{R. L. Dobrushin} and \textit{B. Tirozzi}, Commun. Math. Phys. 54, 173--192 (1977; Zbl 0391.60095) Full Text: DOI OpenURL References: [1] Ibragimov, I. A., Linnik, Ju. V.: Independent and stationary sequences of random variables. Moscow: Nauka 1965. English transl. Groningen: Noordhoff 1971 [2] Statulievicius, V. A.: Proceedings of the International Congress of Mathematics of Vancouver.2, 173 (1974) [3] Riauba, B.: Litovsk. Math. Sb.2, 193 (1962);3, 207 (1963) [4] Khaitov, A.: Proceedings Moscow Math. Soc.28 (1973) [5] Del Grosso, G.: Commun. math. Phys.37, 141 (1974) · Zbl 0363.60110 [6] Minelas, R. A., Halfina, A. M.: Isvestia. A.N. U.R.S.S. Ser. Mat.34, 1173 (1970) [7] Halfina, A. M.: Mat. Sbornik80, 3 (1969) [8] Averinzev, M. B.: Teor. Ver. i ee Prim.17, 21 (1972) [9] Dobrushin, R. L., Minlos, R. A.: Teor. Ver. i ee Prim.12, 595 (1972) [10] Gnedenko, B. V.: Course on probability theory. Moscow: Nauka 1965 [11] Gnedenko, B. V., Kolmogorov, A. N.: Limit distributions for sums of independent random variables. Moscow: Gostechisdat 1949 · Zbl 0056.36001 [12] Thompson, R. L.: Memoirs of the American Mathematical Society 150 (1974) [13] Georgii, H. O.: Z. Wahrscheinlichkeitsth.32, 277 (1975). On canonical Gibbs states and symmetric tail events. Preprint · Zbl 0306.60065 [14] Nakhapitan, B. C.: Dokl. Armianskaia Ak. Nauk. T.61 (1965) [15] Leonenko, W. N.: Cibernetica5, 153 (1975) [16] Masliukova, I. A.: Uce. Sap. Kasanskii Gos. Ped. Inst.9, 81 (1971) [17] Malishev, V. A.: Dokl. Ak. Nauk U.R.S.S.224 (1975) [18] Dobrushin, R. L.: Mat. Sbornik94, 136 (1974) [19] Dobrushin, R. L., Nakhapitan, B. C.: Teor. Mat. Fis.20, 2, 223 (1974) [20] Van Hove, L.: Physica16, 137 (1950) · Zbl 0037.41201 [21] Dobrushin, R. L.: Funz. An.2, 31 (1968) · Zbl 0162.44504 [22] Gallavotti, G., Miracle-Sole, S., Robinson, D.: Phys. Rev. Letters25 A, 493 (1967) [23] Lee, I. D., Yang, E. N.: Phys. Rev.87, 410 (1952) · Zbl 0048.43401 [24] Dobrushin, R. L.: Teor. Mat. Fis.12, I.15 (1972) [25] Dobrushin, R. L.: Teor. Ver. i ee Prim.15, 469 (1970) [26] Ruelle, D.: Statistical Mechanics. [27] Lanford, Q. E.: Lecture notes on physics, No. 2. Berlin-Heidelberg-New York: Springer 1969 [28] Gurevich, B. M.: Teor. Ver. i ee Prim.13, 183 (1968) [29] Khinchin, A. Ia.: Mathematical foundations of statistical mechanics. Moscow: Gostechisdat 1943 [30] Bogoliubov, N. N., Petrina, D. Ia., Khazet, B. I.: Teor. Mat. Fis.1, 251 (1969) [31] Dobrushin, R. L.: Teor. Ver. i ee Prim.17, 619 (1972) [32] Deo, C.: An. Prob.3, 708 (1975) · Zbl 0333.60028 [33] Griffith, R., Ruelle, D.: Commun. math. Phys.23, 169 (1971) · Zbl 0227.76084 [34] Duneau, M., Iagolnitzer, D., Souillard, B.: Commun. math. Phys.35, 307 (1974) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.