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Multi angle Low temperature interfaces and level lines in the critical prewetting regime

Auteurs : Ioffe, Dmitry (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Complete wetting in the context of the low temperature two-dimensional Ising model is characterized by creation of a mesoscopic size layer of the "-" phase above an active substrate. Adding a small positive magnetic field h makes "-"-phase unstable, and the layer becomes only microscopically thick. Critical prewetting corresponds to a continuous divergence of this layer as h tends to zero. There is a conjectured 1/3 (diffusive) scaling leading to Ferrari-Spohn diffusions. Rigorous results were established for polymer models of random and self-avoiding walks under vanishing area tilts.
    A similar 1/3-scaling is conjectured to hold for top level lines of low temperature SOS-type interfaces in three dimensions. In the latter case, the effective local structure is that of ordered walks, again under area tilts. The conjectured scaling limits (rigorously established in the random walk context) are ordered diffusions driven by Airy Slatter determinants.
    Based on joint walks with Senya Shlosman, Yvan Velenik and Vitali Wachtel.

    Codes MSC :
    60F17 - Functional limit theorems; invariance principles
    60G50 - Sums of independent random variables; random walks
    60K35 - Interacting random processes; statistical mechanics type models; percolation theory
    82B41 - Random walks, random surfaces, lattice animals, etc.

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 04/05/2017
      Date de captation : 25/04/2017
      Collection : Research talks
      Format : MP4
      Domaine : Probability & Statistics ; Mathematical Physics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : http://videos.cirm-math.fr/2017-04-25_Ioffe.mp4

    Informations sur la rencontre

    Nom du congrès : Jean-Morlet Chair: Qualitative methods in KPZ universality / Chaire Jean Morlet : Méthodes qualitatives dans la classe d'universalité KPZ
    Organisteurs Congrès : Alberts, Tom ; Bakhtin, Yuri ; Cator, Eric ; Dolgopyat, Dmitry ; Khanin, Konstantin ; Shlosman, Senya
    Dates : 24/04/2017 - 28/04/2017
    Année de la rencontre : 2017
    URL Congrès : http://khanin-shlosman.weebly.com/conference.html

    Citation Data

    DOI : 10.24350/CIRM.V.19161503
    Cite this video as: Ioffe, Dmitry (2017).Low temperature interfaces and level lines in the critical prewetting regime. CIRM . Audiovisual resource .doi:10.24350/CIRM.V.19161503
    URI : http://dx.doi.org/10.24350/CIRM.V.19161503

    Voir aussi


    1. Ioffe, D., & Velenik, Y. (2016). Low-temperature interfaces: Prewetting, layering, faceting and Ferrari-Spohn diffusions. <arXiv:1611.00658> - https://arxiv.org/abs/1611.00658

    2. Ioffe, D., Velenik, Y., & Wachtel, V. (2016). Dyson Ferrari-Spohn diffusions and ordered walks under area tilts. <arXiv:1601.04444> - https://arxiv.org/abs/1601.04444

    3. Ioffe, D., Shlosman, S., & Toninelli, F.L. (2015). Interaction versus entropic repulsion for low temperature Ising polymers. Journal of Statistical Physics, 158(5), 1007-1050 - http://dx.doi.org/10.1007/s10955-014-1153-1