论文标题
随机环境中的约束度渗透
Constrained-degree percolation in random environment
论文作者
论文摘要
我们考虑在平方晶格上随机环境中的约束度渗透模型。在此模型中，每个顶点$ v $都有一个独立的随机约束$κ_V$，该$ j \ in \ {0,1,2,3 \} $带有概率$ρ_j$。每个边缘$ e $尝试在$ [0,1] $中以随机统一时间$ u_e $打开，与所有其他边缘无关。如果在时间$ u_e $时，它的两个最终媒体的学位严格比其附加的约束都要小。我们表明，当$ρ_3$足够大时，该模型会经历非平凡的相变。证明包括脱钩不平等，局部事件的概率的连续性以及粗粒的论点。
We consider the Constrained-degree percolation model in random environment on the square lattice. In this model, each vertex $v$ has an independent random constraint $κ_v$ which takes the value $j\in \{0,1,2,3\}$ with probability $ρ_j$. Each edge $e$ attempts to open at a random uniform time $U_e$ in $[0,1]$, independently of all other edges. It succeeds if at time $U_e$ both its end-vertices have degrees strictly smaller than their respectively attached constraints. We show that this model undergoes a non-trivial phase transition when $ρ_3$ is sufficiently large. The proof consists of a decoupling inequality, the continuity of the probability for local events, and a coarse-graining argument.
