Journal of Applied Probability

Percolation of hard disks

D. Aristoff

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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.

Article information

J. Appl. Probab., Volume 51, Number 1 (2014), 235-246.

First available in Project Euclid: 25 March 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B43: Percolation [See also 60K35] 82B26: Phase transitions (general)

Percolation Poisson point process Gibbs measure grand canonical Gibbs distribution statistical mechanics hard sphere hard disk excluded volume gas/liquid transition phase transition


Aristoff, D. Percolation of hard disks. J. Appl. Probab. 51 (2014), no. 1, 235--246. doi:10.1239/jap/1395771426.

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