(joint work with S. Olla)

We study a one-dimensional hamiltonian chain of masses, perturbed by an energy conserving noise. According to the hamiltonian part of the dynamics, particles move freely in cells and interact with their neighbors through collisions, made possible by a small overlap between near cells. The noise only randomly flips the sign of the velocity of particles. I will first and mainly consider the case where the size ǫ of the overlap region between cells goes to zero, and where time is rescaled by a factor 1/ǫ. We have shown in that case that energy evolves autonomously according to some stochastic equation. If only two different energies are present, the limiting process for the energy actually coincides with the symmetric simple exclusion process. This leads us to think that in a such a case, even when ǫ > 0 is kept constant, the process should converge to a heat equation with a constant diffusion coefficient in the hydrodynamic limit. I’ll then briefly expose the present state of our research on that harder problem.