1206.0725 (Jason Miller et al.)

The Hausdorff dimension of the CLE gasket    [PDF]

Jason Miller, Nike Sun, David B. Wilson

The conformal loop ensemble CLE_kappa is the canonical conformally invariant probability measure on non-crossing loops in a proper simply connected domain in the complex plane. The parameter kappa varies between 8/3 and 8; CLE_{8/3} is empty while CLE_8 is a single space-filling loop. In this work we study the geometry of the CLE gasket, the set of points not surrounded by any loop of the CLE. We show that the almost sure Hausdorff dimension of the gasket is bounded from below by 2-(8-kappa)(3 kappa-8)/(32 kappa) when 4View original: http://arxiv.org/abs/1206.0725