1998/12/31 by John Cardy · 14 citations
Mathematics · Physics and Astronomy · #Boundary (topology) #Brownian motion #Conformal map #Dimension (graph theory) #Distribution (mathematics) #Fractal #Fractal dimension #Hausdorff dimension #Random Matrices and Applications #Random walk #Scaling #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/0305-4470/32/16/001
published in Journal of Physics A Mathematical and General 32(16), L177-L182 (Institute of Physics) · 13 pages. Comments on relation to results in quenched random bulk added, and on relation to other recent work. Typos corrected
openalex publication_date 1999/01/01 · arxiv created 1999/01/05 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The critical behaviour of correlation functions near a boundary is modified from that in the bulk. When the boundary is smooth this is known to be characterized by the surface scaling dimension . We consider the case when the boundary is a random fractal, specifically a self-avoiding walk or the frontier of a Brownian walk, in two dimensions, and show that the boundary scaling behaviour of the correlation function is characterized by a set of multifractal boundary exponents, given exactly by conformal invariance arguments to be . This result may be interpreted in terms of a scale-dependent distribution of opening angles of the fractal boundary: on short distance scales these are sharply peaked around . Similar arguments give the multifractal exponents for the case of coupling to a quenched random bulk geometry.