title: Conformally invariant fractals and potential theory
abstract: The multifractal (MF) distribution of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a Q-state Potts cluster, is solved in two dimensions. The dimension &fcirc;(straight theta) of the boundary set with local wedge angle straight theta is &fcirc;(straight theta) = pi / straight theta-25-c / 12 (pi-straight theta)(2) / straight theta(2pi-straight theta), with c the central charge of the model. As a corollary, the dimensions D(EP) of the external perimeter and D(H) of the hull of a Potts cluster obey the duality equation (D(EP)-1) (D(H)-1) = 1 / 4. A related covariant MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.
authors.affiliation: Service de Physique Theorique de Saclay, F-91191 Gif-sur-Yvette Cedex, France and Institut Henri Poincare, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05, France and and Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, C.
authors.initials: B
authors.lastname: Duplantier