布朗运动、树上的随机游动和多项式朱利亚集上的调和测度
Brownian motion, random walks on trees, and harmonic measure on polynomial Julia sets
摘要：
利用布朗运动研究了不连通多项式朱利亚集上的调和测度.我们证明了这样一个朱利亚集的任何连通分支的调和测度为零。与多项式相关联的是一个组合模型，即动态树。我们在树上定义了一个测度，它是调和测度的组合形式。证明了该测度同构于朱利亚集上的调和测度.该测度诱导树上的随机游动，它同构于平面上的布朗运动。
英文摘要：
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.
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