MODERATE DEVIATIONS OF DEPENDENT RANDOM-VARIABLES RELATED TO CLT

This paper consists of three parts. In the first part, we find a commo n condition-the C-2-regularity-both for CLT and for moderate deviation s. We show that this condition is verified in two important situations : the Lee-Yang theorem case and the FKG system case. In the second par t; we apply the previous results to the additive functionals of a Mark ov process. By means of Feymman-Kac formula and Kato's analytic pertur bation theory, we show that the Lee-Yang theorem holds under the assum ption that 1 is an isolated, simple and the only eigenvalue with modul us 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 statis tical mechanical systems, where the C-2-regularity becomes a property of the pressure functionals and the two situations presented above bec ome exactly the Lee-Yang theorem case and the FKG system case. We shal l discuss in detail the ferromagnetic model and give some general rema rks on some other models.