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Metastability of reversible finite state Markov processes

Author

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  • Beltrán, J.
  • Landim, C.

Abstract

We prove the metastable behavior of reversible Markov processes on finite state spaces under minimal conditions on the jump rates. To illustrate the result we deduce the metastable behavior of the Ising model with a small magnetic field at very low temperature.

Suggested Citation

  • Beltrán, J. & Landim, C., 2011. "Metastability of reversible finite state Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1633-1677, August.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:8:p:1633-1677
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    References listed on IDEAS

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    1. den Hollander, F. & Olivieri, E. & Scoppola, E., 2000. "Nucleation in fluids: some rigorous results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 279(1), pages 110-122.
    2. Gaudillière, A. & den Hollander, F. & Nardi, F.R. & Olivieri, E. & Scoppola, E., 2009. "Ideal gas approximation for a two-dimensional rarefied gas under Kawasaki dynamics," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 737-774, March.
    3. den Hollander, F., 2004. "Metastability under stochastic dynamics," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 1-26, November.
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    Cited by:

    1. Bianchi, Alessandra & Gaudillière, Alexandre, 2016. "Metastable states, quasi-stationary distributions and soft measures," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1622-1680.
    2. Nardi, Francesca R. & Zocca, Alessandro, 2019. "Tunneling behavior of Ising and Potts models in the low-temperature regime," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4556-4575.
    3. Landim, C., 2023. "Metastability from the large deviations point of view: A Γ-expansion of the level two large deviations rate functional of non-reversible finite-state Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 275-315.
    4. Landim, C., 2015. "A topology for limits of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 1058-1088.

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