Laplacian Interface Models with Strictly Convex Potential

N. Kurt

2012, v.18, №1, 9-30


We present an overview of an effective interface model on $Z^d$ with strictly convex potential and interactions depending on the discrete Laplacian. These models are used to describe semiflexible membranes or polymers. We give some basic properties of the model, with a particular focus on the Gaussian case, and compare it to the well-known gradient interface model. To deal with the non-Gaussian case, we derive the Brascamp - Lieb inequality using a Helffer - Sjostrand representation. Furthermore, we prove entropic repulsion for the Laplacian model with strictly convex potential in the supercritical dimensions.

Keywords: random interface models,Laplacian model,entropic repulsion,Brascamp - Lieb inequality,Helffer - Sjostrand representation


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