Surface order large deviations for high-density percolation |
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| Authors: | Jean-Dominique Deuschel Agoston Pisztora |
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| Institution: | (1) Department Mathematik, ETH-Zentrum, CH-8092 Zürich, Switzerland;(2) Present address: TU-Berlin, MA 7-5, Strasse des 17. Juni 135, D-10623 Berlin, Germany;(3) Present address: Department of Mathematics, Harvard University, One Oxford Street, 02138 Cambridge, MA, USA |
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| Abstract: | 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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| Keywords: | 60F10 60K35 82B20 82B43 |
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