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

Abstract

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

20 pages, 7 figures

References in corpus (1)

• On bounded-type thin local sets of the two-dimensional Gaussian free field

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