Thin triangles and a multiplicative ergodic theorem for Teichmüller geometry
Moon Duchin
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.
Create a lesson
Related papers
Combinatorial Goussarov-Polyak-Viro Formulas for the Linking Number and Low Degree Coefficients of the Conway Polynomial
Nancy Scherich, Nathaniel Song
The flip symmetry on Khovanov-Rozansky homology
Hongjian Yang
Families of knots that cannot be made Legendrian parametrically
Javier Martínez-Aguinaga
Branched real projective structures on surfaces and geometrisation of representations
Gianluca Faraco, Nicholas Rungi
Generating the twist subgroup of the level 2 mapping class group of a non-orientable closed surface
Ryoma Kobayashi
H-cobordisms, infinite cyclic covers, and real Seiberg--Witten theory
Sungkyung Kang, JungHwan Park, Masaki Taniguchi