### Metastability for the Dilute Curie-Weiss Model with Glauber Dynamics

Probability Seminar

11th March 2022, 3:30 pm – 4:30 pm

Fry Building, 2.04 (also on zoom)

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 replaced by i.i.d. random coefficients, e.g.

Bernoulli random variables with fixed parameter p. 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 the system size goes

to infinity, the inverse temperature is larger than 1 and the magnetic field 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. This is a joint collaboration with Anton Bovier (Bonn) and

Saeda Marello (Bonn).

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