Mathematical Sciences: Fractal Measures for Random Sets

首席研究员将继续他的工作， 维数的各种度量（例如豪斯多夫和包装 测量）到概率起源的分形对象（特定 随机过程）。 研究者希望延长 理论有两个方向：第一，到子集的d 维晶格和在这个晶格上的随机行走;以及 二是测度值样本路径的研究 扩散 自从物理学的最新发展， 包括分形和它们的维数起着重要的作用， 这项工作可能对物理学家有重要意义。

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.