1998/12/31 by Bertrand Duplantier · 47 citations
Mathematics · Physics and Astronomy · #Algebraic number #Conformal anomaly #Conformal field theory #Conformal map #Fractal #Geometry #Geometry and complex manifolds #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Measure (data warehouse) #Multifractal system #Physics #Quantum mechanics #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.82.880
published in Physical Review Letters 82(5), 880-883 (American Physical Society) · 4 pages, 2 figures, revtex, to appear in Phys. Rev. Lett., January 1999
arxiv created 1998/12/31 · openalex publication_date 1999/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider in two dimensions (2D) the most general star-shaped copolymer, mixing random walks (RW) or self-avoiding walks (SAW) with specific mutual avoidance interactions thereof. Its exact conformal scaling dimensions in the plane are derived from an algebraic structure existing on a random lattice (2D quantum gravity). The multifractal dimensions \ensuremathτ(n) of the harmonic measure of a 2D RW or SAW are conformal dimensions of certain star copolymers. The exact associated f(\ensuremathα) are identical for a RW or a SAW in 2D. These are the first examples of conformal multifractality.