Large deviations for discrete and continuous percolation
Authors:
- Mathew D. PenroseMPMathew D. Penrose
- Agoston PisztoraAPAgoston Pisztora
- 1 March 1996
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 28 (1) , 29-52
Abstract
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.Keywords
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