  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.
