Title: Infinite ergodic index of the ehrenfest wind-tree model,
Abstract: The set of all possible configurations of the Ehrenfest wind-tree model
endowed with the Hausdorff topology is a compact metric space. For a typical
configuration we show that the wind-tree dynamics has infinite ergodic index in
almost every direction. In particular some ergodic theorems can be applied to
show that if we start with a large number of initially parallel particles their
directions decorrelate as the dynamics evolve answering the question posed by
the Ehrenfests.