140 citations · 346 across the 27 of their papers we have counts for
5 papers · 1 filter
The measurable Kesten theorem
Miklos Abert, Yair Glasner, Balint Virag
We give explicit estimates between the spectral radius and the densities of short cycles for finite d-regular graphs. This allows us to show that the essential girth of a finite d-…
The Space of Actions, Partition Metric and Combinatorial Rigidity
Miklos Abert, Gabor Elek
We introduce a natural pseudometric on the space of actions of d-generated groups. In this pseudometric, the zero classes correspond to the weak equivalence classes defined by Kech…
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…
Bernoulli actions are weakly contained in any free action
Miklós Abért, Benjamin Weiss
We show that for any countable group, any free probability measure preserving action of the group weakly contains all Bernoulli actions of the group. It follows that for a finitely…