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

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 $c⩽1$.

arXiv commentPublished version

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Cited by in corpus (4)

• Symmetries of multifractal spectra and field theories of Anderson localization
• The Harmonic Measure of Diffusion-Limited Aggregates including Rare Events
• From combinatorial maps to correlation functions in loop models
• The Harmonic Measure for critical Potts clusters