论文标题
基本证明，在Sierpiński地毯上，布朗尼运动的步行维度大于两个
An elementary proof that walk dimension is greater than two for Brownian motion on Sierpiński carpets
论文作者
论文摘要
我们给出了一个基本的独立证明，证明布朗尼运动在任意广泛的Sierpiński地毯上的步行维度大于两个，而在文献中没有证据证明这一点。我们的证明仅基于相关的迪里奇形式的自相似性和超双立方体对称性，以及几个非常基本的功能分析以及常规对称性迪里奇形式的理论。在这种情况下，我们还提出了有关规范的自相似度量（均匀分布）的能量度量的奇异性的应用，在这种情况下，Hino在[Probab中首先证明了。理论相关领域132（2005），第1期。 2，265-290]。
We give an elementary self-contained proof of the fact that the walk dimension of the Brownian motion on an arbitrary generalized Sierpiński carpet is greater than two, no proof of which in this generality had been available in the literature. Our proof is based solely on the self-similarity and hypercubic symmetry of the associated Dirichlet form and on several very basic pieces of functional analysis and the theory of regular symmetric Dirichlet forms. We also present an application of this fact to the singularity of the energy measures with respect to the canonical self-similar measure (uniform distribution) in this case, proved first by M. Hino in [Probab. Theory Related Fields 132 (2005), no. 2, 265-290].
