60 citations · 76 across the 8 of their papers we have counts for
13 papers
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…
A proof-theoretic metatheorem for tracial von Neumann algebras
Liviu Paunescu, Andrei Sipos
We adapt a continuous logic axiomatization of tracial von Neumann algebras due to Farah, Hart and Sherman in order to prove a metatheorem for this class of structures in the style…
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…
Two special subgroups of the universal sofic group
Matteo Cavaleri, Radu B. Munteanu, Liviu Paunescu
We define a subgroup of the universal sofic group, obtained as the normaliser of a separable abelian subalgebra. This subgroup can be obtained as an extension by the group of autom…
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…
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…
Convex Structures Revisited
Liviu Paunescu
We provide a complete characterisation of extreme points of the space of sofic representations. We also show that the restriction map to , where $H\subset…
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…
A Convex Structure on Sofic Embeddings
Liviu Paunescu
Nathanial Brown introduced a convex-like structure on the set of unitary equivalence classes of unital *-homomorphisms of a separable type II_1 factor into R^ω(ultrapower of the hy…
On Sofic Actions and Equivalence Relations
Liviu Paunescu
The notion of sofic equivalence relation was introduced by Gabor Elek and Gabor Lippner. Their technics employ some graph theory. Here we define this notion in a more operator alge…