论文标题
黄金比率Sierpinski垫圈的布朗运动
Brownian motion on the golden ratio Sierpinski gasket
论文作者
论文摘要
我们通过一项关于无限图上电网络的痕迹的研究，在黄金比例Sierpinski垫圈上构造了强烈的局部常规迪里奇形式，这是一个没有任何有限分支的细胞结构的自相似设置。从无限的迭代功能系统的意义上讲，Dirichlet形式是自相似的，并且相对于以图为导向的结构是不变的。还提供了独特性的定理。最后，相关的过程满足了两侧的高斯次热内核估计值。
We construct a strongly local regular Dirichlet form on the golden ratio Sierpinski gasket, which is a self-similar set without any finitely ramified cell structure, via a study on the trace of electrical networks on an infinite graph. The Dirichlet form is self-similar in the sense of an infinite iterated function system, and is decimation invariant with respect to a graph-directed construction. A theorem of uniqueness is also provided. Lastly, the associated process satisfies the two-sided sub-Gaussian heat kernel estimate.
