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.Codes MSC :
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.
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.