Toeplitz quotient C*-algebras and ratio limits for random walks
Toeplitz quotient C*-algebras and ratio limits for random walks
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发表时间：
2021-04
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通讯作者：
Adam Dor-On
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作者：
Adam Dor-On
我们研究随机游走的 Toeplitz C* 代数的商，类似于作者和 Markiewicz 对有限随机矩阵的研究。我们引入了一种新的 Cuntz 型商 C* 代数，用于具有收敛的转移概率比率的随机游走。这些 C* 代数产生了这种随机游走的比率极限空间和边界的新概念，这些概念是通过引用 Woess 的一篇姊妹篇论文来计算的。我们的综合结果被用来确定双曲群上任何对称随机游走的唯一最小对称等变商 C* 代数，从而阐明 Viselter 关于子积系统 C* 代数的问题。
We study quotients of the Toeplitz C*-algebra of a random walk, similar to those studied by the author and Markiewicz for finite stochastic matrices. We introduce a new Cuntz-type quotient C*-algebra for random walks that have convergent ratios of transition probabilities. These C*-algebras give rise to new notions of ratio limit space and boundary for such random walks, which are computed by appealing to a companion paper by Woess. Our combined results are leveraged to identify a unique smallest symmetry-equivariant quotient C*-algebra for any symmetric random walk on a hyperbolic group, shedding light on a question of Viselter on C*-algebras of subproduct systems.