60 citations · 76 across the 8 of their papers we have counts for
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Constraint stability in permutations and action traces
Goulnara Arzhantseva, Liviu Paunescu
An action trace is a function naturally associated to a probability measure preserving action of a group on a standard probability space. For countable amenable groups, we characte…
Constraint metric approximations and equations in groups
Goulnara Arzhantseva, Liviu Paunescu
We introduce notions of a constraint metric approximation and of a constraint stability of a metric approximation. This is done in the language of group equations with coefficients…
Almost commuting permutations are near commuting permutations
Goulnara Arzhantseva, Liviu Paunescu
We prove that the commutator is stable in permutations endowed with the Hamming distance, that is, two permutations that almost commute are near two commuting permutations. Our res…
All automorphisms of the universal sofic group are class-preserving
Liviu Paunescu
In this article we prove that every automorphism of a universal sofic group is class preserving, i.e. preserves the conjugacy classes
Linear sofic groups and algebras
Goulnara Arzhantseva, Liviu Paunescu
We introduce and systematically study linear sofic groups and linear sofic algebras. This generalizes amenable and LEF groups and algebras. We prove that a group is linear sofic if…