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We consider the random walk loop soup on the discrete half-planecorresponding to a central charge c in (0, 1]. We look at the clusters ofdiscrete loops and show that the scaling limit of the outer boundaries ofoutermost clusters is the CLE(kappa) loop ensemble, with the same relationbetween kappa and c as in the continuum Brownian setting.

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