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Metastability under stochastic dynamics

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  • den Hollander, F.

Abstract

This paper is a tutorial introduction to some of the mathematics behind metastable behavior of interacting particle systems. The main focus is on the formation of so-called critical droplets, in particular, on their geometry and the time of their appearance. Special attention is given to Ising spins subject to a Glauber spin-flip dynamics and lattice particles subject to a Kawasaki hopping dynamics. The latter is one of the hardest models that can be treated to date and therefore is representative for the current state of development of this research area.

Suggested Citation

  • den Hollander, F., 2004. "Metastability under stochastic dynamics," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 1-26, November.
    • Handle: RePEc:eee:spapps:v:114:y:2004:i:1:p:1-26
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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.
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    Cited by:

    1. Nils Berglund & Sébastien Dutercq, 2016. "The Eyring–Kramers Law for Markovian Jump Processes with Symmetries," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1240-1279, December.
    2. 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.
    3. Jing Dong & Pnina Feldman & Galit B. Yom-Tov, 2015. "Service Systems with Slowdowns: Potential Failures and Proposed Solutions," Operations Research, INFORMS, vol. 63(2), pages 305-324, April.

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    1. 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.

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