发表机构
Peking University; The University of Chicago（北京大学; 芝加哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明均匀生成森林中交换不变事件满足零一律，并应用于分量数与过剩端数的恒定性，解决两个长期未决问题。
AI 中文摘要
我们证明，在任意连通的、局部有限的、无限网络上，对于自由或连通的生成森林，任何在交换下不变的事件概率为零或一。应用包括分量数量和总过剩端数量的恒定性。对于自由森林，这些结果解决了Benjamini、Lyons、Peres和Schramm [Ann. Probab. (2001)，问题15.7]关于分量数量恒定性的长期问题，以及Lyons、Morris和Schramm [Electron. J. Probab. (2008)，问题7.7]关于单端性零一律的问题。在后一种情况下，我们得到更强的结论：总过剩端数量是确定性的。
英文摘要
We prove that every event invariant under swaps has probability zero or one for either the free or the wired spanning forest on any connected, locally finite, infinite network. Applications include the constancy of the number of components and of the total number of excessive ends. For the free forest, these results resolve longstanding questions of Benjamini, Lyons, Peres, and Schramm [Ann. Probab. (2001), Question 15.7] on constancy of the component count and of Lyons, Morris, and Schramm [Electron. J. Probab. (2008), Question 7.7] on the zero-one law for one-endedness. In the latter case, we obtain the stronger conclusion that the total number of excessive ends is deterministic.
Comments7 pages, 1 figure
