5 papers
On Krein-Milman theorem for the space of sofic representations
Radu B. Munteanu, Liviu Paunescu
Denote by the space of sofic representations of a countable group . This space is known by a result of the second author, to have a convex-like structure. We show that,…
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…
Unitaries in Ultraproduct of Matrices
Liviu Paunescu
We study various conditions under which a unitary in an ultraproduct of matrices is conjugated to an ultraproduct of permutations.
A generalisation to Birkhoff - von Neumann theorem
Liviu Paunescu, Florin Radulescu
The classic Birkhoff- von Neumann theorem states that the set of doubly stochastic matrices is the convex hull of the permutation matrices. In this paper, we study a generalisation…
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…