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.
The Total Progeny in a Branching Process and a Related Random Walk
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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.