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Applied Math Seminar
Laplacian pinning and wetting models in (1+1)-dimensions
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We consider a random line with a Laplacian interaction and delta-pinning of strength $\epsilon>0$ at the $x$-axis (pinning model) respectively both pinning and repulsion above the $x$-axis (wetting model). Unlike gradient systems with horizontally flat ground states, Laplacian models favor affine configurations and penalize curvature and bending. This model is used in the context of semi-flexible polymers and membranes. We show that this model undergoes pinning and wetting transitions: there are critical pinning, respectively wetting, parameters $\epsilon_i, i=p,w$, such that the interface is delocalized for weak pinning constant $\epsilon<\epsilon_i$ and localized for strong pinning $\epsilon>\epsilon_i$. We also derive a scaling limit theorem for the pinning model in the delocalized regime ($\epsilon<\epsilon_i$) and at criticality ($\epsilon=\epsilon_i$). The proof is based on Markov renewal theory. Joint work with F. Caravenna |