2001/09/26 by M. B. Hastings · 44 citations
Mathematics · Physics and Astronomy · #Ergodic theory #Fractal #Geometry #Harmonic function #Harmonic measure #Invariant (physics) #Invariant measure #Laplace operator #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematical physics #Mathematics #Measure (data warehouse) #Multifractal system #Physics #Quantum mechanics #Random walk #Scaling #Spectral line #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.soft
paper · pdf · doi:10.1103/physrevlett.88.055506
published in Physical Review Letters 88(5), 055506 (American Physical Society) · 4 pages, 3 figures; references added, minor corrections
arxiv created 2001/09/26 · openalex publication_date 2002/01/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Iterated conformal mappings are used to obtain exact multifractal spectra of the harmonic measure for arbitrary Laplacian random walks in two dimensions. Separate spectra are found to describe scaling of the growth measure in time, of the measure near the growth tip, and of the measure away from the growth tip. The spectra away from the tip coincide with those of conformally invariant equilibrium systems with arbitrary central charge c < or = 1, with c related to the particular walk chosen, while the scaling in time and near the tip cannot be obtained from the equilibrium properties.