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LARGE DEVIATIONS FOR DISCRETE AND CONTINUOUS PERCOLATION

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By Mathew D. Penrose and Agoston Pisztora

Motivated by a statistical application,
we consider continuum percolation in two or more dimensions,
restricted to a large finite box, when above the critical point.
We derive surface order large deviation estimates
for the volume of the largest cluster and for its intersection with
the boundary of the box. We also give some natural extensions to known,
analogous results on lattice percolation.
Advances in Applied Probability
28, 29-52 (1997).