A large deviations bound for the Teichmuller flow

TL;DR

This paper establishes large deviation bounds for suspension flows over symbolic systems and applies these results to the Teichmüller flow on moduli spaces, extending previous work by Athreya.

Contribution

It introduces a new large deviation bound for the Teichmüller flow using a method based on symbolic dynamics and Young's approach, extending prior results.

Findings

Large deviation bounds for suspension flows over countable alphabets.

Application of bounds to the Teichmüller flow on moduli spaces.

Extension of earlier large deviation results by Athreya.

Abstract

Large deviation rates are obtained for suspension flows over symbolic dynamical systems with a countable alphabet. The method is that of the first author and follows that of L.-S. Young. A corollary of the main results is a large deviation bound for the Teichm\"uller flow on the moduli space of abelian differentials, which extends earlier work of J. Athreya.