Title: Hilbertian degenerations
Abstract
We study problems involving entities to which a “mass” is attached. This quantity can actually be a mass in the usual sense for systems of particles, but it can also be a thermal capacity in the context of heat transfer, or a kind of charisma in the context of models of opinion dynamics for social media, or the ability of an individual to reach their goal in the context of crowd motion. In all these situations, the considered mass defines a natural Hilbertian metrics useful to characterize the system dynamics. We focus on the case in which the metrics degenerates, i.e. the ratio between different masses tends to infinity. We propose to explore the nature of the limit system corresponding to this degeneration, in all the different situations presented above.
