Random walks on the mapping class group

Abstract

We show that a random walk on the mapping class group of an orientable surface gives rise to a pseudo-Anosov element with asymptotic probability one. Our methods apply to many subgroups of the mapping class group, including the Torelli group.

31 pages, 7 figures. v2: Added references to work of Rivin and I. Kapovich. v3: This version now only contains the mapping class group results. The original application to 3-manifolds contained a gap, which is fixed in arXiv:0809.4881. v4: revised version

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• Train tracks and the Gromov boundary of the complex of curves
• Covers and the curve complex
• A simple criterion for non-relative hyperbolicity and one-endedness of groups
• Counting Reducible Matrices, Polynomials, and Surface and Free Group Automorphisms

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