Thin triangles and a multiplicative ergodic theorem for Teichmüller geometry

Moon Duchin

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Thin triangles and a multiplicative ergodic theorem for Teichmüller geometry

Moon Duchin

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Abstract

We show that, in the Teichmüller metric, "thin-framed triangles are thin"---that is, under suitable hypotheses, the variation of geodesics obeys a hyperbolic-like inequality. This theorem has applications to the study of random walks on Teichmüller space. In particular, an application is worked out for the action of the mapping class group: we show that geodesics track random walks sublinearly.

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Moon Duchin. 2005-08-01. Thin triangles and a multiplicative ergodic theorem for Teichmüller geometry. https://arxiv.org/abs/math/0508046

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