  In this note we show that the transfer operator of a Rauzy-Veech-Zorich
renormalization map acting on a space of quasi-H\"older functions is
quasicompact and derive certain statistical recurrence properties for this map
and its associated Teichm\"uller flow. We establish Borel-Cantelli lemmas,
Extreme Value statistics and return time statistics for the map and flow.
Previous results have established quasicompactness in H\"older or analytic
function spaces, for example the work of M. Pollicott and T. Morita. The
quasi-H\"older function space is particularly useful for investigating return
time statistics. In particular we establish the shrinking target property for
nested balls in the setting of Teichm\"uller flow. Our point of view, approach
and terminology derives from the work of M. Pollicott augmented by that of M.
Viana.
