IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i3p1461-1514.html
   My bibliography  Save this article

Gradient flow approach to local mean-field spin systems

Author

Listed:
  • Bashiri, K.
  • Bovier, A.

Abstract

It is well-known that many diffusion equations can be recast as Wasserstein gradient flows. Moreover, in recent years, by modifying the Wasserstein distance appropriately, this technique has been transferred to further evolution equations and systems; see e.g. Maas (2011), Fathi and Simon (2016), Erbar (2016). In this paper we establish such a gradient flow representation for evolution equations that depend on a non-evolving parameter. These equations are connected to a local mean-field interacting spin system. We then use this gradient flow representation to prove a large deviation principle for the empirical process associated to this system. This is done by using the criterion established in Fathi (2016). Finally, the corresponding hydrodynamic limit is shown by using the approach initiated in Sandier and Serfaty (2004) and Serfaty (2011).

Suggested Citation

  • Bashiri, K. & Bovier, A., 2020. "Gradient flow approach to local mean-field spin systems," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1461-1514.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:3:p:1461-1514
    DOI: 10.1016/j.spa.2019.05.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918304927
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2019.05.006?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bashiri, K. & Menz, G., 2021. "Metastability in a continuous mean-field model at low temperature and strong interaction," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 132-173.

    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:130:y:2020:i:3:p:1461-1514. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.