Statistics of harmonic measure and winding of critical curves from conformal field theory

2008/02/29 by A. Belikov, Andrey V. Belikov, Ilya A. Gruzberg +3
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.1088/1751-8113/41/28/285006

published as J. Phys. A: Math. Theor. 41, 285006 (2008) · Published version

openalex publication_date 2008/06/24 · arxiv created 2008/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Fractal geometry of random curves appearing in the scaling limit of critical two-dimensional statistical systems is characterized by their harmonic measure and winding angle. The former is the measure of the jaggedness of the curves while the latter quantifies their tendency to form logarithmic spirals. We show how these characteristics are related to local operators of conformal field theory and how they can be computed using conformal invariance of critical systems with central charge c ⩽ 1.

Citations

• Stochastic geometry of critical curves, Schramm–Loewner evolutions and conformal field theory
• Critical curves in conformally invariant statistical systems
• A Guide to Stochastic Löwner Evolution and Its Applications