The Hausdorff dimension of the CLE gasket

  title={The Hausdorff dimension of the CLE gasket},
  author={Jason Miller and Nike Sun and David Bruce Wilson},
  journal={Annals of Probability},
  • Jason Miller, Nike Sun, David Bruce Wilson
  • Published 2014
  • Mathematics, Physics
  • Annals of Probability
  • The conformal loop ensemble $\mathrm{CLE}_{\kappa}$ is the canonical conformally invariant probability measure on noncrossing loops in a proper simply connected domain in the complex plane. The parameter $\kappa$ varies between $8/3$ and $8$; $\mathrm{CLE}_{8/3}$ is empty while $\mathrm {CLE}_8$ is a single space-filling loop. In this work, we study the geometry of the $\mathrm{CLE}$ gasket, the set of points not surrounded by any loop of the $\mathrm{CLE}$. We show that the almost sure… CONTINUE READING

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