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Convergence of the two-dimensional random walk loop-soup clusters to CLE. (English) Zbl 07047497
Summary: 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 $$\mathrm{CLE}_{\kappa}$$ conformal loop ensemble.

##### MSC:
 60G15 Gaussian processes 60J67 Stochastic (Schramm-)Loewner evolution (SLE) 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 82B27 Critical phenomena in equilibrium statistical mechanics
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