Groups, drift and harmonic measures

TL;DR

This paper explores harmonic measures for cocompact Fuchsian groups, introducing a new numerical approach to compute drift and measure dimension, providing fresh insights into this classical problem.

Contribution

It presents a novel numerical method to analyze harmonic measures, offering new results on drift and measure dimension for specific examples.

Findings

Numerical computation of drift for cocompact Fuchsian groups

New estimates of measure dimension in specific cases

Enhanced understanding of harmonic measures in hyperbolic geometry

Abstract

In this short note we will describe an old problem and a new approach which casts light upon it. The old problem is to understand the nature of harmonic measures for cocompact Fuchsian groups. The new approach is to compute numerically the value of the drift and, in particular, get new results on the dimension of the measure in some new examples.