IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v165y2023icp275-315.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414923001795
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2023.09.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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. Armendáriz, Inés & Grosskinsky, Stefan & Loulakis, Michail, 2013. "Zero-range condensation at criticality," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3466-3496.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Baldassarri, Simone & Gallo, Anna & Jacquier, Vanessa & Zocca, Alessandro, 2023. "Ising model on clustered networks: A model for opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).
    3. Grosskinsky, Stefan & Jatuviriyapornchai, Watthanan, 2019. "Derivation of mean-field equations for stochastic particle systems," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1455-1475.
    4. 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.
    5. Baldassarri, Simone & Nardi, Francesca R., 2022. "Critical Droplets and sharp asymptotics for Kawasaki dynamics with weakly anisotropic interactions," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 107-144.
    6. Landim, C., 2015. "A topology for limits of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 1058-1088.
    7. 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.
    8. Nicholas M. Ercolani & Sabine Jansen & Daniel Ueltschi, 2019. "Singularity Analysis for Heavy-Tailed Random Variables," Journal of Theoretical Probability, Springer, vol. 32(1), pages 1-46, March.
    9. Bet, Gianmarco & Gallo, Anna & Nardi, F.R., 2024. "Metastability for the degenerate Potts Model with positive external magnetic field under Glauber dynamics," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    10. Mailler, Cécile & Mörters, Peter & Ueltschi, Daniel, 2016. "Condensation and symmetry-breaking in the zero-range process with weak site disorder," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3283-3309.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:165:y:2023:i:c:p:275-315. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.