具有Liouville性质的群上集常返和Green函数的不稳定性
Instability of set recurrence and Green's function on groups with the Liouville property
摘要：
设$μ$和$ν$是群Γ上的概率测度，G_μ和G_ν表示关于μ和ν的格林函数.称群Γ允许格林函数的不稳定性，如果存在对称的、有支撑的测度$μ$和ν以及序列\{x_n\}使得G_μ（e，x_n）/G_ν（e，x_n）\to 0，并且如果存在关于ν是递归的但关于μ是瞬变的集合S，则Γ允许递归的不稳定性。我们给出了一些具有刘维尔性质但同时具有两种不稳定性的群的例子。以前已知的具有这些不稳定性的基团不具有刘维尔性质。
英文摘要：
Let $μ$ and $ν$ be probability measures on a group Γand let G_μand G_νdenote Green's function with respect to μand ν. The group Γis said to admit instability of Green's function if there are symmetric, finitely supported measures $μ$ and νand a sequence \{x_n\} such that G_μ(e, x_n)/G_ν(e,x_n) \to 0, and Γadmits instability of recurrence if there is a set S that is recurrent with respect to νbut transient with respect to μ. We give a number of examples of groups that have the Liouville property but have both types of instabilities. Previously known groups with these instabilities did not have the Liouville property.
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