Title
Multifractal analysis of Gaussian multiplicative chaos and applications
Abstract
A Gaussian Multiplicative Chaos (GMC) is a random measure which can be thought of as the exponential of a log-correlated Gaussian field. The original interest in defining GMC measures stemmed from the need to make rigorous Mandelbrot’s model for energy dissipation in fully developed turbulence, but it has since been found applications in a wide range of fields: from mathematical finance to mathematical physics, but also random matrices as well as number theory. In this talk, I will discuss a result concerning the multifractal nature of GMC measures. In particular, I will show that subcritical GMC measures satisfy the multifractal formalism, and I will present an explicit formula for their singularity spectrum. Finally, I will also discuss a result concerning the lower singularity spectrum of the Liouville Brownian motion.
Please note that the seminar will take place in person in room 140 of Huxley Building.