论文标题
严格的不平等对与柱状疾病的稀晶格上的键渗透性
Strict inequality for bond percolation on a dilute lattice with columnar disorder
论文作者
论文摘要
我们考虑从通常的$ \ mathbb {z}^3 $晶格中获得的稀释晶格，以$ 1-ρ$独立删除其每个列。在剩余的稀释晶格独立的Bernoulli债券渗透中，使用参数$ P $。令$ρ\ mapsto p_c（ρ）$为划分亚临界和超临界阶段的关键曲线。我们研究该曲线在断开连接阈值$ρ_C= p_c^{\ text {site}}}}}}}}}（\ Mathbb {z}^2）$ $附近的行为，并证明，它均匀地超过$ρ$，它严格低于$ 1/2 $（$ 1/2 $（$ 1/2）（对于Squart lattice $ \ mathbbbbbbbbbbbbbbb bys bectiony bots percolation n of $ 1/2 $}
We consider a dilute lattice obtained from the usual $\mathbb{Z}^3$ lattice by removing independently each of its columns with probability $1-ρ$. In the remaining dilute lattice independent Bernoulli bond percolation with parameter $p$ is performed. Let $ρ\mapsto p_c(ρ)$ be the critical curve which divides the subcritical and supercritical phases. We study the behavior of this curve near the disconnection threshold $ρ_c = p_c^{\text{site}}(\mathbb{Z}^2)$ and prove that, uniformly over $ρ$ it remains strictly below $1/2$ (the critical point for bond percolation on the square lattice $\mathbb{Z}^2)$.
