灵活的稳定性和非柔性
Flexible stability and nonsoficity
摘要：
如果对$G$的每个sofic逼近都可以通过修改渐进消失的边比例而转换为Schreier图的不相交并序列，则sofic群$G$被称为灵活稳定的。我们证明了如果$\mathrm{PSL}_d(\mathbb{Z})$对某些$d \geq 5$是灵活稳定的，则存在一个不稳定的群.
英文摘要：
A sofic group $G$ is said to be flexibly stable if every sofic approximation to $G$ can converted to a sequence of disjoint unions of Schreier graphs by modifying an asymptotically vanishing proportion of edges. We establish that if $\mathrm{PSL}_d(\mathbb{Z})$ is flexibly stable for some $d \geq 5$ then there exists a group which is not sofic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
