Cluster Expansion in the Canonical Ensemble

We consider a system of particles confined in a box ${\Lambda \subset \mathbb{R}^d}$ interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low density regime. The convergence is uniform in the volume and in the thermodynamic limit it reproduces Mayer??s virial expansion providing an alternative and more direct derivation which avoids the deep combinatorial issues present in the original proof.