Minicourse:
On fluctuations in interacting particle systems (Hermosillo 2025)
In these talks, we consider a class of interacting particle systems on d dimensional lattices which model 'traffic' broadly understood, e.g. Exclusion and Zero-range systems. We discuss scaled fluctuation limits of local statistics, such as occupation times at sites and the motion of a distinguished, or tagged particle, as well as that of the bulk mass empirical density. A goal is to present some of the ideas in the subject, leading to open problems.
Some notes, in progress, are available in the `Large scale stochastic dynamics' link in the website. In the minicourse, after introduction of some particle systems, We will start with `local' fluctuations of occupation times L8, then of tagged particles L9, going to a brief synopsis of hydrodynamics L2, L3, L4, L5, and then to SPDEs associated to fluctuations of the hydrodynamics L10, L11.