We prove a law of large numbers for the range of rotor walks with random initial configuration on regular trees and on Galton–Watson trees. We also show the existence of the speed for such rotor walks. More precisely, we show that on the classes of trees under consideration, even in the case when the rotor walk is recurrent, the range grows at linear speed.

中文翻译：

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转子在树上行走的范围和速度

我们在常规树和高尔顿-沃森树上证明了具有随机初始配置的转子行走范围的大数定律。我们还展示了这种转子行走速度的存在。更准确地说，我们表明，在所考虑的树木类别上，即使在转子行走是重复的情况下，范围也以线性速度增长。