Brownian motion, random walks on trees, and harmonic measure on polynomial Julia sets
Dynamical Systems
2007-05-23 v2
Abstract
We consider the harmonic measure on a disconnected polynomial Julia set in terms of Brownian motion. We show that the harmonic measure of any connected component of such a Julia set is zero. Associated to the polynomial is a combinatorial model, the tree with dynamics. We define a measure on the tree, which is a combinatorial version on harmonic measure. We show that this measure is isomorphic to the harmonic measure on the Julia set. The measure induces a random walk on the tree, which is isomorphic to Brownian motion in the plane.
Keywords
Cite
@article{arxiv.math/0609044,
title = {Brownian motion, random walks on trees, and harmonic measure on polynomial Julia sets},
author = {Nathaniel D. Emerson},
journal= {arXiv preprint arXiv:math/0609044},
year = {2007}
}
Comments
15 pages, 5 figures. Revised 9/12/06