2005/08/01 by Moon Duchin, Duchin, Moon
Mathematics · #30F60 #37A30 #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DS #math.GT #msc:30F60 #msc:37A30
paper · pdf · doi:10.48550/arxiv.math/0508046
23 pages
arxiv created 2005/08/01 · openalex publication_date 2005/08/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.