Decay of Correlations for the Rauzy-Veech-Zorich Induction Map on the Space of Interval Exchange Transformations and the Central Limit Theorem for the Teichmueller Flow on the Moduli Space of Abelian Differentials

Alexander I. Bufetov

Published 2005-06-12Version 1

A stretched-exponential bound is obtained for the decay of correlations of the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations. A Corollary is the Central Limit Theorem for the Teichmueller flow on the moduli space of abelian differentials. The proof involves an approximation of the induction map by a Markov chain satisfying the Doeblin condition, the method of Sinai and Bunimovich--Sinai. The main estimate is Lemma 4. As a corollary of such "loss of memory" estimates, integrability of a small power of the Kontsevich-Zorich cocycle is obtained, thus yielding a variant of J.Athreya's exponential bound on the probability of returns of the Teichmueller flow into compact sets. An earlier version of this preprint is available from the preprint archive of the Erwin Schroedinger Institute, Vienna, www.esi.ac.at, preprint no.1593 (Jan. 2005).