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Scaling limits of (\(1+1\))-dimensional pinning models with Laplacian interaction. (English) Zbl 1185.60106

The paper deals with a discrete random field with discrete Laplacian interaction and symmetrical, uniformly strictly convex potential. The pinning model is defined by giving the field nonnegative reward each time it touches the \(x\)-axis, that plays the role of a defect line. By using approach based on Markov renewal theory, authors give a precise pathwise description, extracting the full scaling limits of the model.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F05 Central limit and other weak theorems
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
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