Mathematical Sciences: Fractal Measures for Random Sets

数学科学：随机集的分形测度

• 批准号: 9001401
• 负责人: S. James Taylor
• 金额: $ 3.83万
• 依托单位: University of Virginia Main Campus
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001401&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Fractal; Measures; Random

The principal investigator will continue his work relating various measures of dimension (e.g. Hausdorff and packing measures) to fractal objects of probabilistic origin (specific stochastic processes). The investigator wishes to extend the theory in two directions: firstly, to subsets of the d dimensional lattice and random walks on this lattice; and secondly, to the study of the sample paths of measure valued diffusions. Since recent developments in physics in which ideas involving fractals and their dimension play a prominent role, the work could have important implications for physicists.

首席研究员将继续他的工作，将各种维度度量（例如Hausdorff和packing度量）与概率起源（特定随机过程）的分形对象联系起来。研究者希望在两个方向上扩展该理论：首先，扩展到d维晶格的子集和该晶格上的随机行走；其次，对测量值扩散的样本路径进行了研究。由于在物理学的最新发展中，涉及分形及其维度的思想起着突出的作用，这项工作可能对物理学家有重要的意义。