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Explicit upper bounds on the threshold of one-dimensional long-range percolation
We study bond percolation on the one-dimensional lattice in which two sites at distance $r$ are connected with probability $p_r=C/r^{1+σ}$, where $0 < σ< 1$. An infinite cluster exists if $C$ exceeds a critical value $C_c(σ)$, which is not known exactly: the available results are the lower bound of
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