Loop percolation on discrete half-plane

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.

9 pages, 4 figures

References in corpus (3)

• From loop clusters and random interlacement to the free field
• Supercritical loop percolation on ${\mathbb{Z}}^d$ for $d\ge 3$
• Markovian loop clusters on graphs

Cited by in corpus (4)

• The first passage sets of the 2D Gaussian free field: convergence and isomorphisms
• Crossing exponent in the Brownian loop soup
• Percolation for two-dimensional excursion clouds and the discrete Gaussian free field
• 1+O(1) asymptotics for loop percolation in five and higher dimensions