具有慢复杂性的子移位和具有Liouville性质的单群
Subshifts with slow complexity and simple groups with the Liouville property
摘要：
研究子移位的拓扑完全群上的随机游动，证明了具有Liouville性质的无限个单生成单群的存在性。Matui和Juschenko-Monod的结果表明，最小子移位的拓扑完全群的导出子群提供了第一个例子，证明了生成的简单顺从群。我们证明了如果子移位（不一定是最小的）有一个复杂性函数，增长足够慢（例如线性），那么每个对称和拓扑完全群上的支持概率测度有平凡的Poisson-Furstenberg边界。我们也得到了明确的上界的增长的Følner集。
英文摘要：
We study random walk on topological full groups of subshifts, and show the existence of infinite, finitely generated, simple groups with the Liouville property. Results by Matui and Juschenko-Monod have shown that the derived subgroups of topological full groups of minimal subshifts provide the first examples of finitely generated, simple amenable groups. We show that if the (not necessarily minimal) subshift has a complexity function that grows slowly enough (e.g. linearly), then every symmetric and finitely supported probability measure on the topological full group has trivial Poisson-Furstenberg boundary. We also get explicit upper bounds for the growth of Følner sets.
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。
