  We consider a class of deterministic local collisional dynamics, showing how
to approximate them by means of stochastic models and then studying the
fluctuations of the current of energy. We show first that the variance of the
time-integrated current is finite and related to the conductivity by the
Green-Kubo relation. Next we show that the law of the empirical average current
satisfies a large deviations principle and compute explicitly the rate
functional in a suitable scaling limit. We observe that this functional is not
strictly convex.
