About the Jones-Wolff Theorem on the Hausdorff dimension of harmonic measure

TL;DR

This paper provides a detailed, accessible explanation of the Jones-Wolff theorem concerning the Hausdorff dimension of harmonic measure in the plane, aimed at non-expert readers.

Contribution

It offers a comprehensive, pedagogical exposition of the Jones-Wolff theorem, making complex concepts accessible to a broader audience.

Findings

Clarifies the proof of the Jones-Wolff theorem

Explains the relationship between harmonic measure and Hausdorff dimension

Provides insights into planar harmonic measure theory

Abstract

These are the lecture notes of a seminar held at the Universitat Aut\`onoma de Barcelona where the Jones-Wolff theorem about the dimension of harmonic measure in the plane is explained in full detail, for non-expert readers.