论文标题
有限能源无限簇无锚固
Finite-energy infinite clusters without anchored expansion
论文作者
论文摘要
Hermon和Hutchcroft最近证明了一个长期的猜想，即在任何p> p_c（g）上，在伯努利（P）键渗透中，其来源群是有限的，但在n中呈指数呈指数呈指数niffen natifeR n earge。必然的是，所有无限簇几乎肯定都锚定了膨胀。他们询问这些结果是否可以更普遍地保持，以实现任何有限的能量千古不变的渗透。我们给出一个反例，在4型树上不变的渗透。
Hermon and Hutchcroft have recently proved the long-standing conjecture that in Bernoulli(p) bond percolation on any nonamenable transitive graph G, at any p > p_c(G), the probability that the cluster of the origin is finite but has a large volume n decays exponentially in n. A corollary is that all infinite clusters have anchored expansion almost surely. They have asked if these results could hold more generally, for any finite energy ergodic invariant percolation. We give a counterexample, an invariant percolation on the 4-regular tree.
