Metastability For The Dilute Curie-Weiss Model With Glauber Dynamics

ELECTRONIC JOURNAL OF PROBABILITY(2021)

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摘要
We analyse the metastable behaviour of the dilute Curie-Weiss model subject to a Glauber dynamics. The model is a random version of a mean-field Ising model, where the coupling coefficients are Bernoulli random variables with mean p is an element of (0, 1). This model can be also viewed as an Ising model on the Erdos-Renyi random graph with edge probability p. The system is a Markov chain where spins flip according to a Metropolis dynamics at inverse temperature beta. We compute the average time the system takes to reach the stable phase when it starts from a certain probability distribution on the metastable state (called the last-exit biased distribution), in the regime where N -> infinity, beta > beta(c) = 1 and h is positive and small enough. We obtain asymptotic bounds on the probability of the event that the mean metastable hitting time is approximated by that of the Curie-Weiss model. The proof uses the potential theoretic approach to metastability and concentration of measure inequalities.
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关键词
metastability, Glauber dynamics, randomly dilute Curie-Weiss model, Erdos-Renyi random graph
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