Dynamical phase transitions and metastability

In the project we propose thirteen interrelated problems concerned with the behaviour of large systems of dependent random variables. We focus on interacting systems with Markovian dynamics. We are interested both in the reversible case, where the invariant laws are given by Gibbs measures corresponding to an explicit Hamiltonian, and the irreversible case where one has less direct information about the invariant laws. Whether reversible or not, we are mostly interested in dynamical effects.