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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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