JournalsjemsVol. 21, No. 4pp. 1201–1227

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

  • Titus Lupu

    Sorbonne Université, Paris, France
Convergence of the two-dimensional random walk loop-soup clusters to CLE cover

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Abstract

We consider the random walk loop-soup of subcritical intensity parameter on the discrete half-plane H:=Z×N\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 CLEκ_{\kappa} conformal loop ensemble.

Cite this article

Titus Lupu, Convergence of the two-dimensional random walk loop-soup clusters to CLE. J. Eur. Math. Soc. 21 (2019), no. 4, pp. 1201–1227

DOI 10.4171/JEMS/859