Mathematical Sciences: Fractal Measures for Random Sets

首席研究人员将继续他的工作，将各种维度度量(例如Hausdorff度量和填充度量)与概率起源的分形对象(特定随机过程)联系起来。作者希望将这一理论推广到两个方向：第一，d维格的子集及其上的随机游动；第二，研究测值扩散的样本路径。由于最近物理学的发展，涉及分形学及其维度的概念发挥了重要作用，这项工作可能会对物理学家产生重要影响。

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.