Marielle Simone

I started my research career working on one-dimensional systems of interacting oscillators, namely the Hamiltonian dynamics of linear coupled oscillators, which are perturbed by a degenerate conservative stochastic noise. Depending on the choice of the noise, distinct macroscopic phenomena can be rigorously derived: energy diffusion and superdiffusion, as well as a phase transition between these two regimes, by making the noise intensity decrease. A few years later I started working on the weak KPZ universality conjecture, and in particular the extension of the Boltzmann-Gibbs principle (originally designed for one particular stochastic lattice gas) to a significantly wider class of microscopic models. I am also much involved in the mathematical derivation of the moving interfaces problems such as the porous medium equation, through an interdisciplinary long-term scientific project which gathers several researchers from three distinct areas (PDE theory, Theoretical Physics and Probability Theory), and aims at understanding the microscopic mechanisms behind the evolution of some multiphase media. In particular, the rigorous microscopic description of moving interfaces regulated by free boundary problems, the understanding of macroscopic nonlocal effects, and the macroscopic consequences of additional boundary mechanisms, are important matters of my current investigations