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arXiv · 1408.1045

Loop percolation on discrete half-plane

Titus Lupu
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Abstract

We consider the random walk loop soup on the discrete half-plane 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 1/2. The absence of percolation at intensity 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. 2014-08-05. Loop percolation on discrete half-plane. https://doi.org/10.1214/16-ecp4571

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