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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

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  • Landim, C.

Abstract

Consider a sequence of continuous-time Markov chains (Xt(n):t≥0) evolving on a fixed finite state space V. Let In be the level two large deviations rate functional for Xt(n), as t→∞. Under a hypothesis on the jump rates, we prove that In can be written as In=I(0)+∑1≤p≤q(1/θn(p))I(p) for some rate functionals I(p). The weights θn(p) correspond to the time-scales at which the sequence of Markov chains Xt(n) exhibit a metastable behavior, and the zero level sets of the rate functionals I(p) identify the metastable states.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:165:y:2023:i:c:p:275-315
    DOI: 10.1016/j.spa.2023.09.001
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    References listed on IDEAS

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    1. 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.
    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. 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.
    4. Armendáriz, Inés & Grosskinsky, Stefan & Loulakis, Michail, 2013. "Zero-range condensation at criticality," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3466-3496.
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