Date of Degree
Geometry and Topology
geometric topology, random walk, positive drift, Heegaard splitting, mapping class group, compression body graph
A random walk wn 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.
Sunderland, Matthew H., "Linear Progress with Exponential Decay in Weakly Hyperbolic Groups" (2018). CUNY Academic Works.