Percolation of Hard Disks

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 ex...

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Veröffentlicht in:	Journal of applied probability 2014-03, Vol.51 (1), p.235-246
1. Verfasser:	Aristoff, D.
Format:	Artikel
Sprache:	eng
Schlagworte:	60K35 82B26 82B43 Analogies Circles Closed curves Clusters Control equipment Density Disks excluded volume gas/liquid transition Geometric centers Geometric planes Gibbs measure grand canonical Gibbs distribution hard disk Hard disks hard sphere Integers Parameter estimation Particle interactions Percolation phase transition Planes Poisson distribution Poisson point process Poisson process Random variables Statistical mechanics Studies
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Beschreibung
Zusammenfassung:	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.
ISSN:	0021-9002 1475-6072
DOI:	10.1239/jap/1395771426