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.

中文翻译：

---

轨道等价关系的近似同态和索菲克近似

我们证明，对于每个可数群，任何具有排列值的近似同态序列都可以实现为轨道等价关系的 sofic 近似的限制。而且，该轨道等价关系是由近似同态的不变随机子群唯一确定的。我们记录了该结果的应用，以恢复顺应群的几乎同态的各种已知稳定性和共轭特征。