13-22 Y Shang

Continuity of a percolation function on the hierarchical group (312K, Postscript) Mar 4, 13

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Abstract. We consider a long-range 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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