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

Abstract

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.

Citation

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Titus Lupu. "Loop percolation on discrete half-plane." Electron. Commun. Probab. 21 1 - 9, 2016. https://doi.org/10.1214/16-ECP4571

Information

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

Subjects:
Primary: 60K35

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