The limiting equivalence of the canonical and grand canonical ensembles (low density case)

In this paper it is shown that the limiting Gibbs distribution, whose existence was established previously by starting from the grand canonical ensemble, can also be obtained by starting from the canonical ensemble, and both distributions coincide when a certain relation exists between the parameters $\beta$ and $\mu$ (for fixed $\beta$).
The proof is based on the local limit theorem for the number of particles.
Figures: 4.
Bibliography: 12 titles.