The stratum of random mapping classes

DOI10.1017/etds.2016.132zbMath1409.37040arXiv1607.01281OpenAlexW2963069331MaRDI QIDQ4683847

Joseph Maher, Vaibhav Gadre

Publication date: 26 September 2018

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.01281

zbMATH Keywords

random walksmapping class grouppseudo-Anosov mapTeichmüller geodesic

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Generation, random and stochastic difference and differential equations (37H10) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Random walks on graphs (05C81)

Related Items (7)

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Cites Work

• Lattice point asymptotics and volume growth on Teichmüller space
• Hyperbolicity in Teichmüller space
• Word length statistics for Teichmüller geodesics and singularity of harmonic measure
• Counting closed geodesics in moduli space
• Quadratic differentials and foliations
• Random walks on the mapping class group
• Ergodicity of billiard flows and quadratic differentials
• Uniquely ergodic quadratic differentials
• Gauss measures for transformations on the space of interval exchange maps
• Interval exchange transformations and measured foliations
• A compactness theorem for Fuchsian groups of the second kind
• Random walks on weakly hyperbolic groups
• Counting closed geodesics in strata
• Geometry of the complex of curves. I: Hyperbolicity
• The Poisson boundary of the mapping class group
• Sublinear deviation between geodesics and sample paths
• Translation surfaces and their orbit closures: an introduction for a broad audience
• Harmonic measures for distributions with finite support on the mapping class group are singular
• Walks on groups, counting reducible matrices, polynomials, and surface and free group automorphisms
• Statistical hyperbolicity in Teichmüller space
• A train track directed random walk on Out(F_r)
• Spectral Theorems for Random Walks on Mapping Class Groups and Out $(\boldsymbol{F}_{\boldsymbol{N}})$

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