Nonfree actions of countable groups and their characters

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Notes on the Schreier graphs of the Grigorchuk group (2011, background): “Vershik [5] introduced the notion of a totally nonfree action.”
Stabilizers of Ergodic Actions of Lattices and Commensurators (2013, background): “eron 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 nonobvious inv”
Random walks on random coset spaces with applications to Furstenberg entropy (2010, background): “There has been a recent increase in studies of the action of G on SubG and its invariant measures [2–4, 10, 11, 18, 19, 29, 30, 32–34].”
Character rigidity for special linear groups (2013, background): “This character is extremal if the action is ergodic and the stabilizer subgroups are almost everywhere self-normalizing [41], however there are additional extremal characters of this type as well.”
Finite Factor Representations of Higman-Thompson groups (2012, background): “In [20] Vershik suggested that each indecomposable character (an extreme point in the simplex of characters) of a “rich” group G “must” arise as .”