Diffusion rate of windtree models and Lyapunov exponents

Consider a windtree model with several parallel arbitrary right-angled obstacles placed periodically on the plane. We show that its diffusion rate is the largest Lyapunov exponent of some stratum of quadratic differentials and exhibit a new general strategy to compute the generic diffusion rate of such models. This result enables us to compute numerically the diffusion rates of a large family of models, and to observe its asymptotic behaviour according to the shape of the obstacles.