Hydrodynamic Limits and Condensing Zero Range Processes

Explore the intricacies of condensing zero range processes and their hydrodynamic limits in this 45-minute lecture by Marios G. Stamatakis. Delve into the proof of hydrodynamic limits for mean zero condensing zero range processes with bounded local jump rates, focusing on sub-critical initial profiles. Discover how the relative entropy method and a generalized one block estimate contribute to this proof. Examine the challenges in obtaining a closed hydrodynamic equation for general initial profiles, and learn about the non-closed hydrodynamic description derived through relative compactness results. Investigate the behavior of empirical diffusion rates, empirical currents, and empirical densities, and understand how they relate to the continuity equation in the limiting case. Gain insights into the regularity properties of limiting triples and the broader implications of this research in the field of interacting particle systems and phase separation phenomena. This lecture, part of the Hausdorff Trimester Program on Optimal Transportation and its Applications, showcases doctoral research conducted at the University of Crete under the supervision of Professor Michail Loulakis, with support from European Union and national funding initiatives.