Random Walks on Thompson's Group F

Sarah C. Ghandour, Bard College

Abstract/Artist's Statement

In this paper we consider the statistical properties of random walks on Thompson’s group F . We use two-way forest diagrams to represent elements of F . First we describe the random walk of F by relating the steps of the walk to the possible interactions between two-way forest diagrams and the elements of {x_0,x_1}, the finite generating set of F, and their inverses. We then determine the long-term probabilistic and recurrence properties of the walk.