Exponential decay of correlations for finite horizon Sinai billiard flows

We prove exponential decay of correlations for the billiard flow associated with a two-dimensional finite horizon Lorentz Gas (i.e., the Sinai billiard flow with finite horizon). Along the way, we describe the spectrum of the generator of the corresponding semi-group L t of transfer operators, i.e., the resonances of the Sinai billiard flow, on a suitable Banach space of anisotropic distributions.