### On lattice oscillator-type Gibbs systems with superstable many-body potentials

**W. I. Skrypnik**

*Theory of Stochastic Processes*

*Vol.18 (34), no.2, 2012, pp.96-101*

The grand canonical correlation functions of lattice oscillator-type Gibbs systems with a general one-body phase measure space and many-body superstable interaction potentials are found in the thermodynamic limit at low activities as a solution of the ordered lattice Kirkwood--Salzburg equation. For special choices of the measure space, they describe the equilibrium states of lattice classical and quantum linear oscillator systems and the states of stochastic gradient lattice systems of interacting oscillators with Gibbs initial states.