Journal of Applied Probability

Percolation of hard disks

D. Aristoff

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

Dates
First available in Project Euclid: 25 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1395771426

Digital Object Identifier
doi:10.1239/jap/1395771426

Mathematical Reviews number (MathSciNet)
MR3189454

Zentralblatt MATH identifier
1294.60114

Subjects
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)

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

Citation

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


Export citation