Summary
We derive surface order large deviation estimates for the volume of the largest cluster and for the volume of the largest region surrounded by a cluster of a Bernoulli percolation process restricted to a big finite box, with sufficiently large parameter. We also establish a useful version of the isoperimetric inequality, which is the main tool of our proofs.
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Deuschel, JD., Pisztora, A. Surface order large deviations for high-density percolation. Probab. Th. Rel. Fields 104, 467–482 (1996). https://doi.org/10.1007/BF01198162
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DOI: https://doi.org/10.1007/BF01198162
Mathematics Subject Classification (1991)
- 60F10
- 60K35
- 82B20
- 82B43