# Tertychnyi M. V.

### Property of mixing of continuous classical systems with strong superstable interactions

Rebenko A. L., Tertychnyi M. V.

Ukr. Mat. Zh. - 2017. - 69, № 8. - pp. 1084-1095

We consider an infinite system of point particles in $R^d$, interacting via a strong superstable two-body potential $\phi$ of finite range with radius $R$. In the language of correlation functions, we obtain a simple proof of decrease in correlations between two clusters (two groups of variables) the distance between which is larger than the radius of interaction. The established result is true for sufficiently small values of activity of the particles.

### Quasicontinuous approximation in classical statistical mechanics

Petrenko S. M., Rebenko A. L., Tertychnyi M. V.

Ukr. Mat. Zh. - 2011. - 63, № 3. - pp. 369-384

A continuous infinite systems of point particles with strong superstable interaction are considered in the framework of classical statistical mechanics. The family of approximated correlation functions is determined in such a way that they take into account only those configurations of particles in the space $\mathbb{R}^d$ which, for a given partition of $\mathbb{R}^d$ into nonintersecting hypercubes with a volume $a^d$, contain no more than one particle in every cube. We prove that so defined approximations of correlation functions pointwise converge to the proper correlation functions of the initial system if the parameter of approximation a tends to zero for any positive values of an inverse temperature $\beta$ and a fugacity $z$. This result is obtained for both two-body and many-body interaction potentials.