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.
Lace Expansion and Mean-Field Behavior for the Random Connection Model
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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.