PC Seminar: 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. A program for investigating the Fourier decay of the cascade measure was initiated by Mandelbrot and Kahane in the 70's and 90's. Assuming $W$ is sub-exponential, we determine the almost sure Fourier dimension of the cascade measure. We also discuss an analogous problem in higher dimensions and on the circle $S^1\subset\mathbb{R}^2$.

Participte on site or via Zoom link (meeting ID 65089679653).

This is a seminar in our seminar series on Probability and Combinatorics (PC).