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Geodesics track random walks in Teichmuller spaceGeometry/Topology
|Speaker:||Moon Duchin, UCDavis|
|Start time:||Wed, Oct 5 2005, 4:10PM|
We show that almost all random walk trajectories on the mapping class group are well-approximable by Teichmuller geodesic rays. This adapts a similar result of Karlsson and Margulis (1999) -- a version of the Oseledec multiplicative ergodic theorem -- which they proved for Busemann nonpositively curved spaces. In place of this curvature condition (which fails for Teichmuller space), we prove a new comparison-triangle result for the Teichmuller metric.