Limit distribution functions in classical statistical physics

The thermodynamic limit for the partial distribution functions is considered on the basis of Bogolyubov's generating functional method. For one-component systems of hard spheres with binary interaction whose potential at large distances decreases faster than $r_{12}^{-3}$, it is shown that the limit generating functional of the grand canonical ensemble, and when certain “stability conditions” are satisfied, of the canonical ensemble as well: 1) exists in the whole interval of states of the thermodynamic system; 2) defines limit distribution functions; 3) satisfies Bogolyubov's functional equation; 4) can be expanded in a convergent functional Taylor series.