243 citations · 1.7k across the 42 of their papers we have counts for
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Amenability of quadratic automaton groups
Gideon Amir, Omer Angel, Balint Virag
We give lower bounds for the electrical resistance between vertices in the Schreier graphs of the action of the linear (degree 1) and quadratic (degree 2) mother groups on the orbi…
Kesten's theorem for Invariant Random Subgroups
Miklos Abert, Yair Glasner, Balint Virag
An invariant random subgroup of the countable group Γ is a random subgroup of Γ whose distribution is invariant under conjugation by all elements of Γ. We prove that for a nonamena…
Amenability of linear-activity automaton groups
Gideon Amir, Omer Angel, Balint Virag
We prove that every linear-activity automaton group is amenable. The proof is based on showing that a sufficiently symmetric random walk on a specially constructed degree 1 automat…
Amenability via random walks
Laurent Bartholdi, Balint Virag
We answer an open question of Grigorchuk and Zuk about amenability using random walks. Our results separate the class of amenable groups from the closure of subexponentially growin…
Dimension and randomness in groups acting on rooted trees
Miklos Abert, Balint Virag
We explore the structure of the p-adic automorphism group Gamma of the infinite rooted regular tree. We determine the asymptotic order of a typical element, answering an old questi…