Final Report Summary - VARIS (Variational Approach to Random Interacting Systems)
The objects of interest in this project are systems consisting of a large number of random components that interact locally but exhibit a global dependence, resulting in phase transitions and associated critical behaviour. The components are subject to a microscopic dynamics. The challenge lies in understanding the complex macroscopic phenomena that arise from this dynamics. The main approach consists in combining large deviation theory with coarse-graining techniques to derive a variational formula for the probability of the possible trajectories in time of relevant physical quantities. The solution of this variational formula allows for identifying the most likely trajectory, and to describe phase transitions of the system as crossovers in the solution of the variational formula when the parameters of the system are changed.