  In this paper we investigate the speed of convergence of the fluctuations of
a general class of Feynman-Kac particle approximation models. We design an
original approach based on new Berry-Esseen type estimates for abstract
martingale sequences combined with original exponential concentration estimates
of interacting processes. These results extend the corresponding statements in
the classical theory and apply to a class of branching and genealogical
path-particle models arising in nonlinear filtering literature as well as in
statistical physics and biology.
