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A note on truncated long-range percolation with heavy tails on oriented graphs. (arXiv:1709.09757v1 [math.PR])
来源于:arXiv
We consider oriented long-range percolation on a graph with vertex set
$\mathbb{Z}^d \times \mathbb{Z}_+$ and directed edges of the form $\langle
(x,t), (x+y,t+1)\rangle$, for $x,y$ in $\mathbb{Z}^d$ and $t \in \mathbb{Z}_+$.
Any edge of this form is open with probability $p_y$, independently for all
edges. Under the assumption that the values $p_y$ do not vanish at infinity, we
show that there is percolation even if all edges of length more than $k$ are
deleted, for $k$ large enough. We also state the analogous result for a
long-range contact process on $\mathbb{Z}^d$. 查看全文>>