20/04/2022, 17:00 — 18:00 — Online
Cédric Bernardin, Université de Nice
Boundary driven lattice gas with long jumps
Macroscopic Fluctuations Theory (MFT) developed by the « Italian [Brazil as part of Italy included :-)] group » (Bertini et al.) has been one the biggest progress of the last 20 years in our understanding of 1D non-equilibrium stationary states (NESS) of extended interacting particle systems. While the theory has been developed for diffusive and hyperbolic systems (macroscopically), the theory is still not existing for super-diffusive (fractional diffusive) systems. In this talk I will present recent results about the derivation of one-dimensional fractional reaction-diffusion equations with boundary conditions (Dirichlet, Robin, Neuman) for lattice gas with long jumps (mainly the exclusion process) by a hydrodynamic limit procedure. I will also present MFT results for the NESS of the boundary driven zero range process. These results are the first steps in the long-term project to develop MFT for super-diffusive systems. The talk will not be technical (I hope) and its aim is to explain why we are interested in these problems, more than to present the results obtained. (Collaborators: P. Cardoso, P. Gonçalves, B. Oviedo-Jimenez, S. Scotta).
