Groups acting on rooted trees : Dimension, subgroups, randomness and dynamics
This thesis is devoted to the study of different aspects of groups acting on rooted trees and their applications.First, we focus on the Hausdorff dimension of groups acting on rooted trees. We develop new tools that lead to the solution of several well-known open problems in the subject due to Abért-Virág, Bartholdi, Grigorchuk, Klopsch and Shalev among others.Secondly, we study many aspects of thThis thesis is devoted to the study of different aspects of groups acting on rooted trees and their applications.First, we focus on the Hausdorff dimension of groups acting on rooted trees. We develop new tools that lead to the solution of several well-known open problems in the subject due to Abért-Virág, Bartholdi, Grigorchuk, Klopsch and Shalev among others.Secondly, we study many aspects of th
