Conformal radii for conformal loop ensembles
نویسندگان
چکیده
The conformal loop ensembles CLEκ, defined for 8/3 ≤ κ ≤ 8, are random collections of loops in a planar domain which are conjectured scaling limits of the O(n) loop models. We calculate the distribution of the conformal radii of the nested loops surrounding a deterministic point. Our results agree with predictions made by Cardy and Ziff and by Kenyon and Wilson for the O(n) model. We also compute the expectation dimension of the CLEκ gasket, which consists of points not surrounded by any loop, to be 2− (8− κ)(3κ − 8) 32κ , which agrees with the fractal dimension given by Duplantier for the O(n) model gasket.
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