Probabilistic study of interacting particle systems: applications to molecular simulation.

Summary This work presents some results on interacting particle systems for the probabilistic interpretation of partial differential equations, with applications to questions of molecular dynamics and quantum chemistry. In particular, a particle method is presented to analyze the adaptive biasing force process, used in molecular dynamics for the calculation of free energy differences. The sensitivity of stochastic dynamics with respect to a parameter is also studied, in view of the calculation of forces in the Born-Oppenheimer approximation to search for the fundamental quantum state of molecules. Finally, we present a numerical scheme based on a system of particles to solve scalar conservation laws, with an anomalous diffusion term resulting in jump dynamics on the particles.