论文标题
约束度渗透模型
The Constrained-degree percolation model
论文作者
论文摘要
在图$（\ mathbb {v}上的约束度渗透模型中带有分销$ u [0,1] $的随机变量和正整数$ k $。每个债券$ e $都试图在时间$ u_e $上开放，如果其两个最终媒体最多都具有$ k-1 $的学位，则成功。我们证明了该模型在Square Lattice $ \ Mathbb {L}^2 $以及D- ARY常规树上的相变定理。我们还证明，在平方晶格上，无限簇在超临界阶段是独一无二的。
In the Constrained-degree percolation model on a graph $(\mathbb{V},\mathbb{E})$ there are a sequence, $(U_e)_{e\in\mathbb{E}}$, of i.i.d. random variables with distribution $U[0,1]$ and a positive integer $k$. Each bond $e$ tries to open at time $U_e$, it succeeds if both its end-vertices would have degrees at most $k-1$. We prove a phase transition theorem for this model on the square lattice $\mathbb{L}^2$, as well as on the d-ary regular tree. We also prove that on the square lattice the infinite cluster is unique in the supercritical phase.
