Metastability for the dilute Curie-Weiss model with Glauber dynamics

Abstract: Systems subject to a random dynamics exhibit metastability when they persist for a very long time in a phase (called metastable state) that is different from the one corresponding to the thermodynamic equilibrium (called stable state).

In this talk I will analyse the metastable behaviour of the dilute Curie–Weiss model, a classical model of a disordered ferromagnet, subject to a Glauber dynamics. The equilibrium 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.

Under the Glauber dynamics the system is a Markov chain where spins flip according to a Metropolis dynamics at inverse temperature \beta.

I will show how to 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, \beta is larger than 1 and the magnetic field is positive and small enough. I will explain how to 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).

probability

Audience: advanced learners

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Bangalore Probability Seminar

Series comments: The link to zoom meeting can be found on the seminar's google calendar - www.isibang.ac.in/~d.yogesh/BPS.html

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