Discrete Fractal Dimensions and Large Scale Multifractals
主 题: Discrete Fractal Dimensions and Large Scale Multifractals
报告人: 肖益民 (Michigan State University)
时 间: 2015-07-13 16:00 - 17:00
地 点: 理科一号楼 1114
Ordinary fractal dimensions such as Hausdorff dimension and packing dimension are useful for analyzing the (microscopic) geometric structures of various thin sets and measures. For studying (macroscopic or global) fractal phenomena of discrete sets, such as percolation clusters, Barlow and Taylor (1989, 1992) introduced the notions of discrete Hausdorff and packing dimensions. These dimensions have been applied to study random walks and random walks in random environment. In this talk we present some recent results on multifractal properties (in terms of discrete fractal dimensions) of random sets associated with Brownian motion, the Ornstein-Uhlenbeck processes and stochastic partial differential equations. This talk is based on a joint work with Davar Khoshnevisan and Kunwoo Kim.