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abstract: |
    In this paper we study metastable behaviour at low temperature of Glauber spin-flip dynamics on random graphs. We fix a large number of vertices and randomly allocate edges according to the Configuration Model with a prescribed degree distribution. Each vertex carries a spin that can point either up or down. Each spin interacts with a positive magnetic field, while spins at vertices that are connected by edges also interact with each other via a ferromagnetic pair potential. We start from the configuration where all spins point down, and allow spins to flip up or down according to a Metropolis dynamics at positive temperature. We are interested in the time it takes the system to reach the configuration where all spins point up. In order to achieve this transition, the system needs to create a sufficiently large droplet of up-spins, called critical droplet, which triggers the crossover.

    In the limit as the temperature tends to zero, and subject to a certain *key hypothesis* implying metastable behaviour, the average crossover time follows the classical *Arrhenius law*, with an exponent and a prefactor that are controlled by the *energy* and the *entropy* of the critical droplet. The crossover time divided 