Rhythmic behavior in complex stochastic dynamics
Seminario di Finanza Quantitativa e di Probabilità
Interacting particle systems may exhibit, in the thermodynamic limit, a time-periodic behavior in the evolution of their law. We have made an attempt to understand which factors may produce this phenomenon, in particular those related to the time-symmetry breaking of the dynamics: dissipation, delay, asymmetry in the interaction. We will first review some examples of mean field dynamics for which the thermodynamic limit can be explicitly computed and analyzed. Later we will focus on some partial results concerning the first, to our knowledge, example of rhythmic behavior for a system with local interaction: the Ising model with dissipation.