8 papers
Centralizers of sofic approximations of Kazhdan groups
Vadim Alekseev, Andreas Thom
We prove that a Kazhdan group admitting a sofic embedding into a metric ultraproduct of symmetric groups with a centralizer that acts ergodically on the associated Loeb probability…
On non-isomorphic universal sofic groups
Vadim Alekseev, Andreas Thom
We show that there are non-isomorphic universal sofic groups. This proves a conjecture of Simon Thomas.
The hyperfinite II-factor is Ulam stable
Vadim Alekseev, Andreas Thom
We prove Ulam stability of the hyperfinite II-factor with respect to the trace norm on the operator-norm unit ball. More precisely, every sufficiently additive, multiplicative,…
On the asymptotic equidistribution of word values in symmetric groups
Vadim Alekseev, Jakob Schneider, Andreas Thom
We prove an asymptotic equidistribution result for word values for words with constants in the symmetric group. We also speculate about simultaneous asymptotic equidistribution res…
Sofic actions, halo products, and metric approximations of groups
Vadim Alekseev, Henry Bradford
We introduce the notion of a ``sofic -action'' of one group on another by automorphisms, for a class of groups. We show that if is the clas…
Remarks on approximability and stability for groups
Vadim Alekseev, Andreas Thom
In this paper, we provide several instances in which interesting approximation and stability properties are inherited by quotients with respect to finitely generated normal subgrou…