论文标题
超临界渗透簇的瞬态和锚定等方维度
Transience and anchored isoperimetric dimension of supercritical percolation clusters
论文作者
论文摘要
我们建立了伯诺利键渗透恒定簇的锚定等级簇的等效特征。我们将这些特征与Duminil-Copin，Goswami，Raoufi，Severo和Yadin的定理一起推断出，如果$ G $是瞬态的瞬态图表，那么$ G $的无限元素将是$ p $的$ p $ the $ p $的瞬时。它仍然开放，将此结果扩展到关键概率。在此过程中，我们建立了具有独立利益的两个新的集群排斥不平等。
We establish several equivalent characterisations of the anchored isoperimetric dimension of supercritical clusters in Bernoulli bond percolation on transitive graphs. We deduce from these characterisations together with a theorem of Duminil-Copin, Goswami, Raoufi, Severo, and Yadin that if $G$ is a transient transitive graph then the infinite clusters of Bernoulli percolation on $G$ are transient for $p$ sufficiently close to $1$. It remains open to extend this result down to the critical probability. Along the way we establish two new cluster repulsion inequalities that are of independent interest.
