Fluctuations in the dilute Curie-Weiss model

The dilute Curie-Weiss model is the Ising model on a (dense) Erdös-Rényi graph G(N,p). It was introduced by Bovier and Gayrard in 1990s. There the authors showed that on the level of laws of large numbers the magnetization as well as the free energy behave as they do in the usual Curie-Weiss model (i.e. mean-field Ising model). We analyze CLTs for the these quantities and give several critical values for p at which these fluctuations change. This is joint work with Zakhar Kabluchko and Kristina Schubert.