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Loop percolation on discrete half-plane

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arxiv 1408.1045 v3 pith:HRRIKHGO submitted 2014-08-05 math.PR

classification math.PR
keywords percolationdiscretehalf-planeintensitylooploopsabsencebound
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. (Non-)coincidence of critical parameters for Poisson Zoos and Loop Soup Percolation on $\mathbb{Z^d}$, $d > 4$, and $\mathbb{T}_d$,$ d \ge 3$

    math.PR 2026-08 accept novelty 7.0 of 10

    Loop soup percolation on Z^d, d≥5, has discrete threshold strictly above the cable system threshold 1/2; on trees, Poisson zoo percolation and susceptibility thresholds coincide, and the model is infinitesimally sensi...

  2. Loop clusters on complete graphs

    math.PR 2025-04 conditional novelty 6.0 of 10

    In the loop soup on the complete graph K_n, the number of clusters of size d converges to a mixed Poisson law with mixing variable exp(-dZ/κ), and clusters larger than n^{1-ε} appear almost surely.

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