This talk is concerned with the macroscopic fractal and multifractal behavior of various (discrete or non-discrete) random sets that arise from random walks, Brownian motion, Gaussian processes, and the solutions to SPDEs. In particular, we study (i) Macroscopic dimensions of the ranges of random walks in random environment; (ii) Tall peaks of Brownian motion; and (iii) Macroscopic multifractal properties of the OU process and stochastic heat equations.

 

This talk is based on joint papers with Davar Khoshnevisan (University of Utah), Kunwoo Kim (POSTECH), and Xinghua Zheng (HKUST).