The Scaling Limit of the $$(\nabla +\Delta )$$-Model

Cipriani, Alessandra; Dan, Biltu; Hazra, Rajat Subhra

doi:10.1007/s10955-021-02717-1

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2023

Publication Types

Select...

Other1

Article1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where V 1 and V 2 are potentials characterizing the membrane's lateral tension and bending rigidity (see [8] and references therein). The membrane model is also interesting due to its scaling properties, especially in the critical dimension d = 4, which plays a role analogous to that dimension 2 plays for the discrete GFF.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic and Scaling Limits of the non-Gaussian Membrane Model

Thoma¹

2021

Preprint

View full text Add to dashboard Cite

We characterize the behavior of a random discrete interface φ on [−L, L] d ∩ Z d with energyV (∆φ(x)) as L → ∞, where ∆ is the discrete Laplacian and V is a uniformly convex, symmetric, and smooth potential. The interface φ is called the non-Gaussian membrane model. By analyzing the Helffer-Sjöstrand representation associated to ∆φ, we provide a unified approach to continuous scaling limits of the rescaled and interpolated interface in dimensions d = 2, 3, Gaussian approximation in negative regularity spaces for all d ≥ 2, and the infinite volume limit in d ≥ 5. Our results generalize some of those of [7].

show abstract

Section: Introductionmentioning

confidence: 99%