Ensemble dependence of fluctuations and the canonical/micro-canonical equivalence of ensembles
  We study the equivalence of microcanonical and canonical ensembles in
continuous systems, in the sense of the convergence of the corresponding Gibbs
measures. This is obtained by proving a local central limit theorem and a local
large deviations principle. As an application we prove a formula due to
Lebowitz-Percus-Verlet. It gives mean square fluctuations of an extensive
observable, like the kinetic energy, in a classical micro canonical ensemble at
fixed energy.
