Metastability for General Dynamics with Rare Transitions: Escape Time and Critical Configurations

@article{Cirillo2014MetastabilityFG,
  title={Metastability for General Dynamics with Rare Transitions: Escape Time and Critical Configurations},
  author={Emilio N. M. Cirillo and Francesca R. Nardi and Julien Sohier},
  journal={Journal of Statistical Physics},
  year={2014},
  volume={161},
  pages={365-403}
}
Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with statistical mechanics systems, this phenomenon has been described in an elegant way in terms of the energy landscape associated to the Hamiltonian of the system. In this paper, we provide a similar description in the general rare transitions setup. Beside their theoretical… 
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33 Citations
Background Citations
17
Methods Citations
11
Results Citations
1

33 Citations

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References

SHOWING 1-10 OF 41 REFERENCES

Metastability in stochastic dynamics of disordered mean-field models

Abstract. We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise…

Metastability for a Stochastic Dynamics with a Parallel Heat Bath Updating Rule

We consider the problem of metastability for a stochastic dynamics with a parallel updating rule with single spin rates equal to those of the heat bath for the Ising nearest neighbors interaction. We…

Metastability: A Potential-Theoretic Approach

Metastability is an ubiquitous phenomenon of the dynamical behaviour of complex systems. In this talk, I describe recent attempts towards a model-independent approach to metastability in the context…

Metastability for Reversible Probabilistic Cellular Automata with Self-Interaction

The problem of metastability for a stochastic dynamics with a parallel updating rule is addressed in the Freidlin–Wentzel regime, namely, finite volume, small magnetic field, and small temperature.…

Metastable behavior of stochastic dynamics: A pathwise approach

In this paper a new approach to metastability for stochastic dynamics is proposed. The basic idea is to study the statistics of each path, performing time averages along the evolution. Metastability…

Tunneling and Metastability of Continuous Time Markov Chains II, the Nonreversible Case

We proposed in Beltrán and Landim (J. Stat. Phys. 140:1065–1114, 2010) a new approach to prove the metastable behavior of reversible dynamics based on potential theory and local ergodicity. In this…

Fast Mixing for the Low Temperature 2D Ising Model Through Irreversible Parallel Dynamics

We study tunneling and mixing time for a non-reversible probabilistic cellular automaton. With a suitable choice of the parameters, we first show that the stationary distribution is close in total…

Competitive nucleation in metastable systems

Metastability is observed when a physical system is close to a first order phase transition. In this paper the metastable behavior of a two state reversible probabilistic cellular automaton with…

Metastability and small eigenvalues in Markov chains

In this Letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerably…

On the Essential Features of Metastability: Tunnelling Time and Critical Configurations

AbstractWe consider Metropolis Markov chains with finite state space and transition probabilities of the form $$P(\eta ,\eta ')=q(\eta ,\eta ')e^{- \beta [H(\eta ') - H(\eta)]_+}$$ for given energy…