Decay of covariances, uniqueness of ergodic component and scaling limit for a class of \(\nabla\phi\) systems with non-convex potential

DOI10.1214/11-AIHP437zbMath1247.60133arXiv0807.2621WikidataQ114060567 ScholiaQ114060567MaRDI QIDQ441251

Codina Cotar, Jean-Dominique Deuschel

Publication date: 20 August 2012

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.2621

zbMATH Keywords

scaling limitsurface tensiondecay of covarianceseffective non-convex gradient interface modelsuniqueness of ergodic component

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Second-order elliptic equations (35J15) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24)

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Cites Work

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• Existence of random gradient states
• Scaling limit for a class of gradient fields with nonconvex potentials
• Strict convexity of the free energy for a class of non-convex gradient models
• Grad \(\phi\) perturbations of massless Gaussian fields
• Localization and delocalization of random interfaces
• Gibbs measures and phase transitions
• Rosenthal's inequality for LPQD sequences
• On the correlation for Kac-like models in the convex case
• Algebraic \(L^ 2\) decay of attractive critical processes on the lattice
• Motion by mean curvature from the Ginzburg-Landau \(\nabla\phi\) interface model
• Large deviations and concentration properties for \(\nabla_\varphi \) interface models
• Equilibrium fluctuations for \(\nabla\varphi\) interface model
• On homogenization and scaling limit of some gradient perturbations of a massless free field
• On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to \(\nabla\varphi\) interface model
• Phase coexistence of gradient Gibbs states
• The ergodic theorem for additive cocycles of ℤ^d or ℝ^d

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