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Relations between cumulants of random fields with an attraction. (Russian) Zbl 0666.60047
The notions of random fields with an attraction are introduced. The author proposes a general method that will allow to obtain relations between semi-invariants of this fields. This method yields correlation inequalities formulated in a hypothetical way ten years ago [see e.g. C. M. Neuman, Commun. Math. Phys. 41, No.1, 1–9 (1975), and J. Feldman, Can. J. Phys. 52, No.6, 1583–1587 (1974; Zbl 1371.83072)].
The proof is based on representations of the statistical sums and the correlation functions by means of random graphs. These inequalities can be used for the proof of the central limit theorem (with a nonclassical norm) for some Ising models.
Reviewer: D.Aissani

60G60 Random fields