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Percolation of Hard Disks

Part of: Special processes Equilibrium statistical mechanics

Published online by Cambridge University Press:  30 January 2018

D. Aristoff
D. Aristoff*
Affiliation:
University of Minnesota
*
∗ Postal address: Department of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church Street SE, Minneapolis, MN 55455, USA, Email address: daristof@umn.edu
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Abstract

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Random arrangements of points in the plane, interacting only through a simple hard-core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process. It is proved that, at high intensity, an infinite connected cluster of excluded volume appears almost surely.

Keywords

PercolationPoisson point processGibbs measuregrand canonical Gibbs distributionstatistical mechanicshard spherehard diskexcluded volumegas/liquid transitionphase transition

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 82B43: Percolation 82B26: Phase transitions (general)

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 1 , March 2014 , pp. 235 - 246
Copyright
© Applied Probability Trust 

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