Multiplicative chaos and multiplicative cascades
Hubert Lacoin (IMPA)

Multiplicative cascades were introduced in the 70s by Mandelbrot and Yaglom as a canonical model for self-similar fractal random measures. While initially designed by Yaglom as a model for turbulence, the richness of the model made it very popular in statistical mechanics, in particular in the spin glass community. In the 80s, Kahane introduced Gaussian Multiplicative Chaos which generalizes multiplicative cascades and received a renewed interest in the last decade as a fundamental building brick in the mathematical theory of Liouville Quantum Gravity. The aim of this talk is to review some classical results concerning Gaussian Multiplicative Chaos in the simpler context of multiplicative cascades, and introduce some more recent results we have obtain studying this object in a complex setup. [Based on joint work with R. Rhodes (Marseille) and V. Vargas (Paris).]