Non-equilibrium Dynamics and Random Matrices

Fluctuations of the current of one dimensional non equilibrium diffusive systems are well understood. After a short review of the one dimensional results, the talk will try to show that the statistics of these fluctuations are exactly the same in higher dimension, for arbitrary geometries. This result can be established by a mapping between the variational problem in finite dimension and in one dimension. In the particular case of the symmetric exclusion process, the statistical properties of the current are the same as those of disordered quantum wires in the metallic regime, where the distribution of the transmission coefficients of the different channels have been predicted from the theory of random matrices.