Abstract: We consider classical continuous system of interacting particles in Euclidean space (classical gas). Our approach to the limit theorems for the particle number is based on the method of cluster expansions which is well known for nite Gibbs processes. In case of the limiting Gibbs process with empty boundary conditions, we use our result on the cluster representation of such processes which goes back to Malyshev and Minlos. We prove integral and local central limit theorems for a large class of stable and regular pair potentials (which include physically relevant interactions) if the activity is small. In case of local central limit theorem we obtain also an estimate of convergence rate.
Giada Basile | mailto: basile@mat.uniroma1.it |
Domenico Monaco | mailto: monaco@mat.uniroma1.it |