Subshifts with slow complexity and simple groups with the Liouville property
Subshifts with slow complexity and simple groups with the Liouville property
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具有缓慢复杂性和具有 Liouville 性质的简单群的子移
DOI：
10.1007/s00039-014-0293-4
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发表时间：
2014
影响因子：
2.2
通讯作者：
Nicolás Matte Bon
中科院分区：
文献类型：
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作者：
Nicolás Matte Bon
研究了子移位的拓扑满群上的随机游动，证明了具有Liouville性质的无限单生成群的存在性。Matui和Juschenko-Monod的结果表明，最小子移位的拓扑全群的导出子群提供了第一个例子，证明了简单顺从群。我们表明，如果（不一定是最小的）子移位有一个复杂性函数，增长足够缓慢（例如线性），那么每个对称和支持概率测度的拓扑全群平凡泊松-Furstenberg边界。我们也得到明确的上界的增长的Følner集。
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.