Abstract:We study rotor walk, a deterministic counterpart of the simple random walk, on infinite transient graphs. We show that the final rotor configuration of the rotor walk (after the walker escapes to infinity) follows the law of the wired uniform spanning forest oriented toward infinity (OWUSF) measure when the initial rotor configuration is sampled from OWUSF. This result holds for all graphs for which each tree in the wired spanning forest has one single end almost surely. This answers a question posed in a previous work of the author (Chan 2018).

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中文翻译：

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转子行走和跨接林的无限步平稳性

摘要：我们在无限的瞬态图上研究转子游走，这是简单随机游走的确定性对应物。我们显示，当从OWUSF采样初始转子配置时，转子行走的最终转子配置（在助行器逃逸到无穷大之后）遵循面向无限（OWUSF）测度的有线均匀跨越森林的定律。这个结果适用于几乎所有图表，在这些图表中，有线生成林中的每一棵树几乎都具有一个单端。这回答了作者先前的工作（Chan 2018）中提出的一个问题。

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