%0 Journal Article
%T Brownian motion, random walks on trees, and harmonic measure on polynomial Julia sets
%A Nathaniel D. Emerson
%J Mathematics
%D 2006
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0609044v2