Moderate Deviations of Dependent Random Variables Related to CLT

This paper consists of three parts. In the first part, we find a common condition-the C 2 -regularity-both for CLT and for moderate deviations. We show that this condition is verified in two important situations: the Lee-Yang theorem case and the FKG system case. In the second part, we apply the previous results to the additive functionals of a Markov process. By means of Feynman-Kac formula and Kato's analytic perturbation theory, we show that the Lee-Yang theorem holds under the assumption that 1 is an isolated, simple and the only eigenvalue with modulus 1 of the operator P 1 acting on an appropriate Banach space (bE, C b (E), L 2 ... ). The last part is devoted to some applications to statistical mechanical systems, where the C 2 -regularity becomes a property of the pressure functionals and the two situations presented above become exactly the Lee-Yang theorem case and the FKG system case. We shall discuss in detail the ferromagnetic model and give some general remarks on some other models.