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  1. ; (, Ergodic Theory and Dynamical Systems)
    Abstract We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence relation is uniquely determined by the invariant random subgroup of the approximate homomorphisms. We record applications of this result to recover various known stability and conjugacy characterizations for almost homomorphisms of amenable groups. 
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  2. ; (, Mathematische Zeitschrift)
    Abstract In this paper we exhibit for every non amenable group that is initially sub-amenable (sometimes also referred to as LEA), two sofic approximations that are not conjugate by any automorphism of the universal sofic group. This addresses a question of Pǎunescu and generalizes the Elek–Szabo uniqueness theorem for sofic approximations. 
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