Wind-tree model for billiard motion from a signal processing viewpoint

In the Ehrenfest wind tree model, a point particle moves on the plane and collides with randomly placed fixed square obstacles under the usual law of geometric optics. The particle represents the wind and the squares are the trees. We examine the periodic version of the model. Previous authors analyze the dynamical properties of the model using techniques from algebraic topology or ergodic theory. In contrast to these works, we adopt a signal processing viewpoint. We describe the phenomenon of the long-term trajectories by using a 3-state hidden Markov model.