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Large deviations for discrete and continuous percolation

Part of: Special processes Limit theorems Stochastic processes Equilibrium statistical mechanics

Published online by Cambridge University Press:  01 July 2016

Mathew D. Penrose  and
Agoston Pisztora
Mathew D. Penrose*
Affiliation:
University of Durham
Agoston Pisztora
Affiliation:
Courant Institute, New York University
*
* Postal address: Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE, UK.
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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

CONTINUUM PERCOLATIONLARGE DEVIATIONSSUPERCRITICAL PHASEPOISSON PROCESS

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 60F10: Large deviations 82B43: Percolation
Secondary: 60G55: Point processes 82B21: Continuum models (systems of particles, etc.)
Type
Stochastic Geometry amd Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 1 , March 1996 , pp. 29 - 52
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

**

Present postal address: Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA 02138, USA.

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