Speaker: Ville Suomala
Title: Fourier dimension of Mandelbrot multiplicative cascades
Abstract:
Canonical Mandelbrot cascades are well-known random measures on the unit interval, exhibiting detailed multifractal structure. Their construction relies on a single non-negative random variable $W$ with unit expectation. Assuming $W$ is sub-exponential, we determine the almost sure Fourier dimension of the cascade measure. We also discuss an analogous problem on the circle $S^1\subset\mathbb{R}^2$. This talk is based on joint work with Changhao Chen and Bing Li.