Ressearch interest

My main interests (for the moment) are the derivation of kinetic equation from many body particles systems. In particular I want to understand the apparition of irreversibility in determinisitic system.

During my PhD I worked on low density limits. The particles can interact only at short distance but very strongly. Hence each collision mix a little bit the system. The typical example of such system is a large billard of N hard identical spheres, each of of diameter ε. The interesting ratio between ε and N is Nε² = 1 (when we are in dimension 3). When the number of particles goes to infinity the system is discribe by the Boltzmann equation.

Now I work on an other interesting example is the mean-field system: the particles interact at long distance (of size 1) but weakly (the straigth of the interaction is of order 1/N). If you look at these system on time of order 1, it stays reversible (it describe by the Vlasov equation). However due to the mixing effects, the system becomes irreversible on long time (of order N). The system may be described by the Lennard-Balescu equation.