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Random Walks On Thompson's Group F, Sarah C. Ghandour
Random Walks On Thompson's Group F, Sarah C. Ghandour
Senior Projects Fall 2016
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 {x0,x1}, the finite generating set of F, and their inverses. We then determine the long-term probabilistic and recurrence properties of the walk.