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Full-Text Articles in Mechanical Engineering
The Scaling Limit Of The Membrane Model, Alessandra Cipriani, Biltu Dan, Rajat Subhra Hazra
The Scaling Limit Of The Membrane Model, Alessandra Cipriani, Biltu Dan, Rajat Subhra Hazra
Journal Articles
On the integer lattice, we consider the discrete membrane model, a random interface in which the field has Laplacian interaction. We prove that, under appropriate rescaling, the discrete membrane model converges to the continuum membrane model in d ≥ 2. Namely, it is shown that the scaling limit in d = 2, 3 is a Holder continuous random field, while in d ≥ 4 the membrane model converges to a random distribution. As a by-product of the proof in d = 2, 3, we obtain the scaling limit of the maximum. This work complements the analogous results of Caravenna and …