## Section: New Results

### Multifractal analysis

Participants : Julien Barral, Xiong Jin, Yan-Hui Qu.

#### Multiplicative cascades

Part of this work is done in cooperation with Benoît Mandelbrot (Yale University).

The results obtained concern the following topics: Multifractal analysis of complex random cascades [21] , Fractional multiplicative processes [24] , Uniform convergence of [0, 1] -martingales [23] , Convergence of signed multiplicative cascades [22] , Dynamics of Mandelbrot cascades [25] .

#### Multifractal analysis and Geometric measure theory

The results obtained concern the following topics:

Multifractal analysis for projections of Gibbs and related measures. This is done in cooperation with Imen Bhouri (Monastir University) [65] .

In cooperation with IStéphane Seuret: Multifractal analysis, large deviations, and localized asymptotic behavior for almost additive potentials [67] , A pure jump Markov process with a random singularity spectrum [66] , The singularity spectrum of the inverse of Cookie-Cutters [26] .