发表机构
Bocconi University; Northwestern University（博科尼大学; 西北大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在度数至少为3的正则树上，伯努利键逾渗中无限簇的出现严格早于绝对连续谱，结合Bordenave定理得到$p_c<p_{ac}<1$。
AI 中文摘要
对于度数至少为3的每一棵正则树上的伯努利键逾渗，我们证明了无限簇严格出现在绝对连续谱之前。在一个明确的超临界区间内，每个开簇的邻接算子几乎必然没有绝对连续分量。结合Bordenave定理，这给出了$p_c<p_{ac}<1$。
英文摘要
For Bernoulli bond percolation on every regular tree of degree at least three, we prove that infinite clusters appear strictly before absolutely continuous spectrum. Throughout an explicit supercritical interval, the adjacency operator of every open cluster almost surely has no absolutely continuous component. Together with Bordenave's theorem, this gives $p_c<p_{ac}<1$.
