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Surface order large deviations for high-density percolation
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  • Published: December 1996

Surface order large deviations for high-density percolation

  • Jean-Dominique Deuschel1 nAff2 &
  • Agoston Pisztora1 nAff3 

Probability Theory and Related Fields volume 104, pages 467–482 (1996)Cite this article

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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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Author information

Author notes
  1. Jean-Dominique Deuschel

    Present address: TU-Berlin, MA 7-5, Strasse des 17. Juni 135, D-10623, Berlin, Germany

  2. Agoston Pisztora

    Present address: Department of Mathematics, Harvard University, One Oxford Street, 02138, Cambridge, MA, USA

Authors and Affiliations

  1. Department Mathematik, ETH-Zentrum, CH-8092, Zürich, Switzerland

    Jean-Dominique Deuschel & Agoston Pisztora

Authors
  1. Jean-Dominique Deuschel
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  2. Agoston Pisztora
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Cite this article

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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  • Received: 19 December 1994

  • Revised: 18 September 1995

  • Issue Date: December 1996

  • DOI: https://doi.org/10.1007/BF01198162

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Mathematics Subject Classification (1991)

  • 60F10
  • 60K35
  • 82B20
  • 82B43
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