Raphael Lefevere
Paris Diderot University 

Ever since the works of the founding fathers of statistical mechanics, the derivation of the laws of macroscopic transport as the result of the motion of the microscopic components has been a major challenge which remains largely unsolved to this day. I will present a new model that can be seen as a random lattice Lorentz gas and for which a macroscopic diffusion equation can be rigorously derived from the microscopic dynamics.  The proof is based on the fact that in high dimension, random walks have a small probability of making loops or intersecting each other when starting sufficiently far apart.