The scaling limit of the membrane model

Cipriani, Alessandra ; Dan, Biltu ; Hazra, Rajat Subhra (2019) The scaling limit of the membrane model Annals of Probability, 47 (6). pp. 3963-4001. ISSN 0091-1798

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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 Hölder 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 Deuschel (Ann. Probab. 37 (2009) 903–945) in d=1.

Item Type:Article
Source:Copyright of this article belongs to Institute of Mathematical Statistics.
Keywords:Continuum Membrane Model; Green’s Function; Membrane Model; Random Interface; Scaling Limit.
ID Code:121025
Deposited On:08 Jul 2021 10:53
Last Modified:08 Jul 2021 10:53

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