 1322 Y Shang
 Continuity of a percolation function on the hierarchical group
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Mar 4, 13

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Abstract. We consider a longrange percolation in the hierarchical group
$\Omega_N$ of order $N$ where probability of connection between two
nodes separated by distance $k$ is of the form
$\min\{lphaeta^{k},1\}$, $lpha\ge0$ and $eta>0$. The
percolation function $ heta(lpha,eta)$ is defined as the
probability of having a infinite component contain the origin ${f
0}\in\Omega_N$. We show that $ heta(lpha,eta)$ is continuous
with respect to both $lpha$ and $eta$.
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