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Metastability is a phenomenon that occurs in the dynamics of a multi-stable non-linear system subject to noise. It is characterized by the existence of multiple, well separated time scales. The talk will be focus on the metastable behavior of the dilute Curie-Weiss model, that is a Ising spin system on a Erdos-Renyi random graph with $N$ vertices and retention probability $p \in (0,1)$. Each spin interacts with a external field, while the interaction among neighbouring spin variables is assumed to be of the same strength. In particular, I will discuss bounds on the mean exit time from the metastable to the stable state and the spectral gap.
