Some topics in the dynamics of group actions on rooted trees

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Notes on the Schreier graphs of the Grigorchuk group (2011, methodology): “In Section 7 we apply the results of the previous sections to the study of the Grigorchuk group and prove Theorems 1.1 and 1.2.”
Milnor's Problem on the Growth of Groups and its Consequences (2011, methodology): “ere used and continue to be used in diﬀerent situations: in the study of amenable groups [95, 101], in topology [81], in theory of random walks on groups [76, 136, 72], in theory of operator algebras [110, 112, 109], in dynamical systems [23, 46], in percolation [175], the study of cellular automata”
Stabilizers of Ergodic Actions of Lattices and Commensurators (2013, background): “ 4). Bergeron and Gaboriau [BG04] observed that invariant random subgroups behave similarly to normal subgroups and this topic has attracted much recent attention: [ABB+11], [AGV14], [Bow12], [GS12], [Gri11], [Ver11], [Ver12]. Our work, like that of Stuck and Zimmer, rules out the existence of nonob”