Linear Progress with Exponential Decay in Weakly Hyperbolic Groups

Author

Matthew H. Sunderland, The Graduate Center, City University of New YorkFollow

Date of Degree

9-2018

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Joseph Maher

Committee Members

Abhijit Champanerkar

Jason Behrstock

Tobias Johnson

Subject Categories

Geometry and Topology

Keywords

geometric topology, random walk, positive drift, Heegaard splitting, mapping class group, compression body graph

Abstract

A random walk w_n on a separable, geodesic hyperbolic metric space X converges to the boundary ∂X with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes positive linear progress. Progress is known to be linear with exponential decay when (1) the step distribution has exponential tail and (2) the action on X is acylindrical. We extend exponential decay to the nonacylindrical case. We give an application to random Heegaard splittings.

Recommended Citation

Sunderland, Matthew H., "Linear Progress with Exponential Decay in Weakly Hyperbolic Groups" (2018). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/2790