Decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations and the central limit theorem for the Teichmüller flow on the moduli space of Abelian…

By Alexander I. Bufetov. 2005

65 citations recorded by the source corpus.

The aim of this paper is to prove a stretched-exponential bound for the decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations (Theorem 4). A corollary is the Central Limit Theorem for the Teichm?ller flow on the moduli space of abelian differentials with prescribed singularities (Theorem 10). The proof of Theorem 4 proceeds by the method of Sinai [13] and Bunimovich Sinai [14]: the induction map is approximated by a sequence of Markov chains satisfying the Doeblin condition. The main "loss of memory" estimate is Lemma 4.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2c4f991467e7228c7139f3a4495c9b10dc41978f

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In Applied Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Quantitative recurrence and large deviations for Teichmüller geodesic flow (2005, background): “Other interesting results concerning deviations are due to Bufetov [ 2 ], who proved a central limit theorem for this flow.”
Limit theorems for translation flows (2008, methodology): “We will use Veech’s representation of abelian differentials by zippered rectangles, and in this section we recall Veech’s construction using the notation of [11], [15].”