Convergence of the two-dimensional random walk loop-soup clusters to CLE

Source abstract

We consider the random walk loop-soup of subcritical intensity parameter on the discrete half-plane \mathtt{H}:=\mathbb{Z}\times\mathbb{N} . We look at the clusters of discrete loops and show that the scaling limit of the outer boundaries of outermost clusters is a CLE _{\kappa} conformal loop ensemble.