Sublinear deviation between geodesics and sample paths

Abstract

We give a proof of the sublinear tracking property for sample paths of random walks on various groups acting on spaces with hyperbolic-like properties. As an application, we prove sublinear tracking in Teichmueller distance for random walks on mapping class groups, and on Cayley graphs of a large class of finitely generated groups.

23 pages. Added section on lamplighter groups over trees and various minor revisions. Refereed version

References in corpus (2)

• On laws of large numbers for random walks
• Thin triangles and a multiplicative ergodic theorem for Teichmüller geometry

Cited by in corpus (12)

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• Ergodic decompositions for folding and unfolding paths in Outer space
• Random veering triangulations are not geometric
• Spectral theorems for random walks on mapping class groups and $\text{Out}(F_N)$
• Volumes of random 3-manifolds
• The Smallest Positive Eigenvalue Of Fibered Hyperbolic 3-Manifolds
• Small eigenvalues of random 3-manifolds
• Central limit theorem and geodesic tracking on hyperbolic spaces and Teichmüller spaces
• Uniform models and short curves for random 3-manifolds
• Equidistribution of closed geodesics along random walk trajectories with respect to the harmonic invariant measure
• Random walks on the discrete affine group
• Sublinearly Morse Boundary II: Proper geodesic spaces