Guy Amit

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 $p_r=C/r^{1+\sigma}$, where $0<\sigma<1$. An infinite cluster exists if $C$ exceeds a critical value $C_c(\sigma)$, which is not known exactly: the available results are the lower bound of Schulman...