发表机构
Rice University（莱斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
利用Hastings-Levitov二维DLA公式，证明调和测度多分形谱第三矩的普适振幅与团簇分形维数之间的精确关系。
AI 中文摘要
几十年来，已知扩散限制聚集团簇调和测度的多分形谱第三矩与团簇的底层分形维数相关。我们利用基于二维扩散限制聚集（DLA）的Hastings-Levitov公式的论证，展示了更强的联系，将第三矩的普适振幅与团簇分形维数联系起来。该论证可用于标准圆形DLA以及圆柱体（即具有周期性边界条件）中的DLA。
英文摘要
It has been known for several decades that the third moment of the multifractal spectrum of the harmonic measure for diffusion-limited aggregates is linked to the underlying fractal dimension of the cluster. We demonstrate, using an argument based on the Hastings-Levitov formulation of diffusion-limited aggregation (DLA) in two dimensions, an even stronger link, connecting the universal amplitude of the third moment to the cluster fractal dimension. This argument can be used for both the standard circular DLA as well as DLA in a cylinder (i.e., with periodic boundary conditions); in the latter case the relationship of the amplitude to the fractal dimension is weaker, and must be extracted via a scaling analysis.
Comments7 pages, 3 figures; revision of previously posted arXiv submission, corrected white space
