In the Poisson random connection model, largest component size is logarithmic in window volume subcritically and linear supercritically, with exponential tails for subcritical clusters at the origin.
A new proof of the sharpness of the phase transition for Bernoulli percolation on Zd
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Largest component and sharpness in continuum percolation
In the Poisson random connection model, largest component size is logarithmic in window volume subcritically and linear supercritically, with exponential tails for subcritical clusters at the origin.