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 $c⩽1$.

Published version

References in corpus (5)

• 2D growth processes: SLE and Loewner chains
• A Guide to Stochastic Loewner Evolution and its Applications
• Stochastic geometry of critical curves, Schramm-Loewner evolutions, and conformal field theory
• Conformal Fractal Geometry and Boundary Quantum Gravity
• Critical curves in conformally invariant statistical systems

Cited by in corpus (2)

• From combinatorial maps to correlation functions in loop models
• The Harmonic Measure for critical Potts clusters