Open Access
2016 Loop percolation on discrete half-plane
Titus Lupu
Electron. Commun. Probab. 21: 1-9 (2016). DOI: 10.1214/16-ECP4571


We consider the random walk loop soup on the discrete half-plane $\mathbb{Z} \times \mathbb{N} ^{\ast }$ and study the percolation problem, i.e. the existence of an infinite cluster of loops. We show that the critical value of the intensity is equal to $\frac{1} {2}$. The absence of percolation at intensity $\frac{1} {2}$ was shown in a previous work. We also show that in the supercritical regime, one can keep only the loops up to some large enough upper bound on the diameter and still have percolation.


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Titus Lupu. "Loop percolation on discrete half-plane." Electron. Commun. Probab. 21 1 - 9, 2016.


Received: 22 September 2015; Accepted: 22 January 2016; Published: 2016
First available in Project Euclid: 5 April 2016

zbMATH: 1338.60235
MathSciNet: MR3485399
Digital Object Identifier: 10.1214/16-ECP4571

Primary: 60K35

Keywords: loop percolation , random walk loop soup

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