Harmonic measure and winding of random conformal paths: A Coulomb gas perspective

TL;DR

This paper uses Coulomb gas methods to derive multifractal exponents related to harmonic measure and winding of conformally invariant random paths, extending previous quantum gravity results to multiple-path configurations.

Contribution

It introduces Coulomb gas techniques to rederive and extend multifractal exponents for harmonic measure and winding in SLE paths, including multiple-path star configurations.

Findings

Rederived mixed multifractal exponents using Coulomb gas methods.

Extended results to multiple paths in star configurations.

Connected Coulomb gas approach with previous quantum gravity findings.

Abstract

We consider random conformally invariant paths in the complex plane (SLEs). Using the Coulomb gas method in conformal field theory, we rederive the mixed multifractal exponents associated with both the harmonic measure and winding (rotation or monodromy) near such critical curves, previously obtained by quantum gravity methods. The results also extend to the general cases of harmonic measure moments and winding of multiple paths in a star configuration.