UVictoria Probability and Dynamics Seminar: Vicente Lenz

We analyse the metastable behaviour of the disordered Curie-Weiss-Potts (DCWP) model subject to a Glauber dynamics. The model is a randomly disordered version of the mean-field q-spin Potts model (CWP), where the interaction coefficients between spins are general independent random variables. This model comprises also, e.g., the CWP model on inhomogeneous dense random graphs. We are interested in a comparison of the metastable behaviour of the CWP and the DCWP models, for fixed temperature and the infinite volume limit. We prove the CWP model is metastable and through this prove metastability for the DCWP model. 

Then we identify the ratio of the (random) mean time the DCWP model takes to reach the stable phase when it starts from a certain probability distribution on the metastable state (called the last-exit biased distribution) and the (non-random) corresponding quantity for the CWP model. In particular, we obtain the asymptotic tail behaviour and the moments of the ratio of the metastable hitting times of the disordered and annealed systems. Our proof is based on a combination of the potential theoretic approach to metastability and concentration of measure techniques, the later adapted to our particular setup.