140 citations · 346 across the 27 of their papers we have counts for
16 papers · 1 filter
Rank, combinatorial cost and homology torsion growth in higher rank lattices
Miklos Abert, Tsachik Gelander, Nikolay Nikolov
We investigate the rank gradient and growth of torsion in homology in residually finite groups. As a tool, we introduce a new complexity notion for generating sets, using measured…
A Spectral Strong Approximation Theorem for Measure Preserving Actions
Miklos Abert
Let be a finitely generated group acting by probability measure preserving maps on the standard Borel space . We show that if is a subgroup with relative spectr…
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…
Hyperfinite actions on countable sets and probability measure spaces
Miklos Abert, Gabor Elek
We introduce the notion of hyperfiniteness for permutation actions of countable groups on countable sets and give a geometric and analytic characterization, similar to the known ch…
On the growth of Betti numbers of locally symmetric spaces
Miklos Abert, Nicolas Bergeron, Ian Biringer +4
We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uni…
Most actions on regular trees are almost free
Miklos Abert, Yair Glasner
Let T be a d-regular tree (d > 2) and A=Aut(T), its automorphism group. Let G be a group generated by n independent Haar-random elements of A. We show that almost surely, every non…