Linear progress in the complex of curves

TL;DR

This paper proves that a random walk on the mapping class group of a surface makes linear progress in the complex of curves, demonstrating predictable growth behavior in a geometric setting.

Contribution

It establishes that random walks on the mapping class group exhibit linear progress in the complex of curves, linking probabilistic behavior with geometric properties.

Findings

Random walk on the mapping class group makes linear progress in the complex of curves.

Progress is quasi-isometric to the relative metric.

Results connect probabilistic group actions with geometric structures.

Abstract

We show that a random walk on the mapping class group of an orientable surface of finite type makes linear progress in the relative metric, which is quasi-isometric to the complex of curves.