The construction of the \(d+1\)-dimensional Gaussian droplet

DOI10.1007/BF02102597zbMath0858.60096MaRDI QIDQ1924052

Gérard Ben Arous, Jean-Dominique Deuschel

Publication date: 13 October 1996

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

asymptotic behavior of a Gaussian random fieldquadratic variational problemrandom hypersurfaces

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44)

Related Items (15)

Entropic repulsion and the maximum of the two-dimensional harmonic crystal. ⋮ Imaginary geometry. I: Interacting SLEs ⋮ Imaginary geometry. III: Reversibility of \(\mathrm{SLE}_\kappa\) for \(\kappa \in (4,8)\) ⋮ The Kardar-Parisi-Zhang equation as scaling limit of weakly asymmetric interacting Brownian motions ⋮ Scaling limits for weakly pinned Gaussian random fields under the presence of two possible candidates ⋮ Critical region for droplet formation in the two-dimensional Ising model ⋮ Fluctuations for the Ginzburg-Landau \(\nabla \phi\) interface model on a bounded domain ⋮ Entropic repulsion of the lattice free field. II: The \(0\)-boundary case ⋮ Thick points of the Gaussian free field ⋮ Extremes of the discrete two-dimensional Gaussian free field ⋮ Quantitative homogenization of the disordered \(\nabla \phi \) model ⋮ Imaginary geometry. II: Reversibility of \(\operatorname{SLE}_{\kappa}(\rho_{1};\rho_{2})\) for \(\kappa\in(0,4)\) ⋮ Rigorous probabilistic analysis of equilibrium crystal shapes ⋮ Rigorous probabilistic analysis of equilibrium crystal shapes ⋮ Large deviations for the \(\nabla\varphi\) interface model with self potentials

Cites Work

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• On the microscopic validity of the Wulff construction and of the generalized Young equation
• Positively correlated normal variables are associated
• Critical large deviations for Gaussian fields in the phase transition regime. I
• Entropic repulsion of the lattice free field
• Langevin dynamics of spreading and wetting

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