Conformal radii for conformal loop ensembles

Details Conformal radii for conformal loop ensembles Conformal radii for conformal loop ensembles

2006-11-22

arxiv.org/abs/math/0611687v4

Commun.Math.Phys.288:43-53,2009

Mathematics

Probability

12 pages, v4 updates references

Scientific paper

10.1007/s00220-009-0731-6

The conformal loop ensembles CLE(k), defined for k in [8/3, 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 CLE(k) gasket, which consists of points not surrounded by any loop, to be 2-(8-k)(3k-8)/32k, which agrees with the fractal dimension given by Duplantier for the O(n) model gasket.

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