Salem Samir

In this talk, I will discuss a method to derive macroscopic models from interacting particles systems with jumping trajectories and singular interaction. This method is based on a compactness argument and a control on an "information" quantity. It enables to reach singularities which were not covered by the already existing literature,
but provides only a qualitative convergence result from the particle system towards the macroscopic limit. The models we deal with are the
fractional Keller-Segel model, which arises in the description of the chemotaxis of bacteria, and the Boltzmann equation with soft potentials.