Room P3.31, Mathematics Building

Clément Erignoux, INRIA Lille
Varadhan's non-gradient method for diffusive hydrodynamic limits II

For several decades, entropy methods have provided robust tools to derive the hydrodynamic limit of various interacting lattice gases. In the diffusive case, however, these tools depend on the so-called gradient condition, that ensures the generator of the process acts as a local laplacian. Whenever this condition is not satisfied, the local distribution of the process is perturbed, which induces changes to the macroscopic behavior of the system. In this mini-course, I will try and explain, without going through all the technical details, Varadhan's non-gradient method to derive the scaling limit of non-gradient diffusive lattice gases. The focus will be on the structure of the proof and the main ideas and concepts that make the proof work, while skipping some of the more technical aspects.